Wen-Xiu Ma

Teaching and Research:

Teaching:

Teaching interests:

Differential Equations, Real Analysis, Mathematical Physics, Applied Mathematics, Symbolic Computations.

Courses taught at University of South Florida include: 

College Algebra, Calculus, Ordinary Differential Equations, Partial Differential Equations,Real Analysis, Complex Variables, Methods of Mathematical Physics, Applications of Lie Groups to Differential Equations, Lie Algebras and Applications, Applied Partial Differential Equations, and Symbolic Computations.

Research:

• Integrable Systems, Soliton Theory, Orthogonal Polynomials, Symbolic Computations


• International Workshop on Nonlinear and Modern Mathematical Physics, July 15-21 2009, Shihezi, Xinjiang, China


• 7th International Conference on Differential Equations and Dynamical Systems, December 15-18, 2010, Tampa, Florida, USA


• Fast Breaking Paper:W. X. Ma, Variational identities and applications to Hamiltonian structures of soliton equations, Nonlinear Analysis: Theory, Methods & Applications, Vol.71(2009), e1716-e1726  


• Special Invitation from the Academy of Nonlinear Sciences:

During WCNA 2012 held in Athens, Greece, our session speakers were invited to submit articles related to their talks to journals published by ANS. Please do not hesitate to contact Professor L. K. Kuzmina ([email protected]) if there is any question regarding the submission matter.

• 2nd International Workshop on Nonlinear and Modern Mathematical Physics, March 9-11, 2013, Tampa, Florida, USA


• Most Cited Paper:W. X. Ma, T. W. Huang and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application, Physica Scripta, Vol.82(2010), 065003


• Best Paper appearing in SCM: W. X. Ma, A refined invariant subspace method and applications to evolution equations, Science China Mathematics, Vol.55(2012), 1796-1778  Best Paper Award


• 3rd International Workshop on Nonlinear and Modern Mathematical Physics, April 9-11, 2015, Cape Town, South Africa


• Highly Cited Researcher: Included in Clarivate Analytics' annual highly cited researchers list since 2015


• 4th International Workshop on Nonlinear and Modern Mathematical Physics, May 4-8, 2017, Kuala Lumpur, Malaysia


• 5th International Workshop on Nonlinear and Modern Mathematical Physics, May 20-24, 2019, Honolulu, HI, USA

Editorial Boards:

• Editor-in-Chief of Journal of Applied Mathematics and Physics


• Co-Editor-in-Chief of Studies in Nonlinear Sciences


• Editorial Advisory Board of Open Mathematics


• Editor-in-Chief of Asian Journal of Mathematics and Physics


• Editor-in-Chief of International Journal of Complexity


• Editor-in-Chief of International Journal of Engineering Mathematics and Physics


• Editor-in-Chief of Partial Differential Equations in Applied Mathematics


• Advances in Applied Mathematics and Mechanics


• Advances in Mathematical Physics


• Advances in Mathematical Sciences Journal


• Annual Review of Chaos Theory, Bifurcations and Dynamical Systems


• Antarctica Journal of Mathematics


• British Journal of Applied Science & Technology


• British Journal of Mathematics & Computer Science


• Communications in Numerical Analysis


• Far East Journal of Applied Mathematics


• Global Journal of Mathematical Sciences


• Global Journal of Pure and Applied Mathematics


• International Journal of Applied Mathematics & Statistics


• International Journal of Differential Equations


• International Journal of Mathematical Analysis


• International Journal of Modern Physics B


• International Journal of Nonlinear Dynamical Systems


• Journal of Advances in Applied Mathematics


• Journal of Engineering and Applied Mathematics


• Journal of Mathematical Sciences: Advances and Applications


• Journal of Nonlinear Systems and Applications


• Journal of Pure and Applied Mathematics: Advances and Applications


• Mathematics


• Modern Physics Letters B


• Open Journal of Applied Sciences


• Pacific Journal of Applied Mathematics


• Progress in Applied Mathematics


• Results in Nonlinear Analysis


• Studies in Mathematical Sciences


• Turkish Journal of Physics


• Journal of Nonlinear Mathematical Physics 1999-2002


• Communications in Nonlinear Science and Numerical Simulation 2010-2012

Journals of Interest

• Applied Mathematics and Computation


• Chaos, Solitons & Fractals


• Communications in Mathematical Physics


• Computers & Mathematics with Applications


• International Journal of Modern Physics B


• Inverse Problems


• Journal of Geometry and Physics


• Journal of Mathematical Physics


• Journal of Nonlinear Mathematical Physics


• Journal of Physics A: Mathematical and Theoretical


• Modern Physics Letters B


• Nonlinear Analysis


• Nonlinear Analysis: Real World Applications


• Nonlinear Dynamics


• Nonlinearity


• Physics Letters A

Favorite Webpages

• Community of Science in Baltimore, Maryland


• ISI Web of Knowledge at the Institute for Scientific Information


• MacTutor History of Mathematics Archive at School of Mathematical and Computational Sciences, University of St Andrews, Scotland


• Mathematics Department Web Servers available within Math on the Web


• Mathematics Journals compiled by Mathematical Reviews staff


• MathSciNet developed by American Mathematical Society


• Nonlinear Science Archive at Los Alamos National Laboratory


• ScienceDirect designed by Elsevier Science


• The Solitons Homepage at Department of Mathematics, Heriot-Watt University, Edinburgh

Publications

Before 1991:

• W. X. Ma, On the two sorts of Hamiltonian operators, Journal of Graduate School of University of Science and Technology of China and Academia Sinica, Vol.3(1986), No.3, 37--48(in Chinese)


• W. X. Ma, The equivalent conditions of several u-nonlinear Hamiltonian operators, Journal of Shanghai Jiaotong University, Vol.21, No.5(1987), 99--108(in Chinese) (MR 88m:58082)


• W. X. Ma, The generalized Hamiltonian structure of a hierarchy of nonlinear evolution equations, Kexue Tongbao, Vol.32, No.14(1987), 1003--1004


• W. X. Ma, On the periodic functions without the least positive period, Mathematics in Practice and Theory, 1988:3, 45--51(in Chinese) (MR 90c:26001)


• W. X. Ma, A hierarchy of evolution equations with three Hamiltonian structures and its symmetries, Journal of Shanghai Jiaotong University, Vol.23, No.1(1989), 9--18(in Chinese) (MR 90i:58076)


• W. X. Ma, A new involutive system of polynomials and its classical Integrable Systems, Chinese Science Bulletin, Vol.35, No.22(1990), 1853--1858 (MR 94i:58087)


• W. X. Ma, K-symmetries and τ-symmetries of evolution equations and their Lie algebras, Journal of Physics A: Mathematical and General, Vol.23, No.13(1990), 2707--2716 (MR 91d:58220)


• W. X. Ma, Poisson manifolds and classical Hamiltonian operators, Northeastern Mathematical Journal, Vol.6, No.3(1990), 346--356 (MR 92e:58071)


• W. X. Ma, Some Hamiltonian operators in the infinite-dimensional Hamiltonian systems, Acta Mathematicae Applicatae Sinica, Vol.13, No.4,(1990), 484--496 (in Chinese) (MR 92f:58061)


• W. X. Ma, A new method of generating classical integrable systems, The Chinese Youth Society of Mechanics Symposium of the Fourth Annual Conference, Science Press, Beijing, 1990, 516--520(in Chinese)


• W. X. Ma, Some finite-dimensional involutive systems with polynomial forms, Journal of Mathematical Research and Exposition, Vol.10. No.4(1990), 509--515(in Chinese) (MR 91j:58079)


• W. X. Ma, The confocal involutive systems and the integrability of the nonlinearized Lax systems of AKNS hierarchy, Nonlinear Physics, Research Reports in Physics, Springer-Verlag, Berlin, 1990, 79--84 (MR 93a:58084)

1991-1995:

• W. X. Ma, Generators of vector fields and time dependent symmetries of evolution equations, Science in China A, Vol.34, No.7(1991), 769--782 (MR 92i:58077)


• W. X. Ma, Commutational representations of Yang hierarchy of integrable evolution equations, Chinese Science Bulletin, Vol.36, No.16(1991), 1325--1330 (MR 93e:58088)


• W. X. Ma, A new approach for finding Lax representations of evolution equation hierarchies, Journal of Fudan University (Natural Science), Vol.30, No.3(1991), 304--311 (in Chinese) (MR 93h:58072)


• W. X. Ma, Isospectral Lax operators and related algebraic structures, Selected Papers of Chinese Postdoctors, Vol.4, Beijing University Press, 1991, 1--13(in Chinese)


• W. X. Ma, A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems, Applied Mathematics and Mechanics, Vol.13, No.4(1992), 369--377 (MR 93i:58075)


• W. X. Ma, A new hierarchy of Liouville integrable generalized Hamiltonian equations and its reduction, Chinese Annals of Mathematics, Series A, Vol.13, No.1(1992), 115--123; Chinese Journal of Contemporary Mathematics, Vol.13, No.1(1992), 79--89 (MR 94g:58100)


• G. Z. Tu and W. X. Ma, An algebraic approach for extending Hamiltonian operators, Journal of Partial Differential Equations, Vol.3, No.1(1992), 53--56 (MR 93a:58094)


• W. X. Ma, The algebraic structure related to L-A-B triad representations of integrable systems, Chinese Science Bulletin, Vol.37, No.15(1992), 1249--1253


• W. X. Ma, An approach for constructing nonisospectral hierarchies of evolution equations, Journal of Physics A: Mathematical and General, Vol.25(1992), L719--L726 (MR 93c:35151)


• W. X. Ma, The algebraic structures of isospectral Lax operators and applications to integrable equations, Journal of Physics A: Mathematical and General, Vol.25(1992), 5329--5343 (MR 94c:58088)


• W. X. Ma, Lax operator algebras associated with Lax representations of integrable systems, Chinese Science Bulletin, Vol.37, No.14(1992), 1229--1231


• W. X. Ma, Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations, Journal of Mathematical Physics, Vol.33, No.7(1992), 2464--2476 (MR 93h:58073)


• W. X. Ma, The product property of the generators of vector fields, Nature Journal, Vol.15, No.5 (1992), 391--392(in Chinese)


• W. X. Ma, Laurent polynomial spectral problem, nonisospectral flows and symmetry algebra, Proceedings of CSIAM Second Conference, Shanghai, 1992, 466--469


• W. X. Ma, Isospectral Lax operator algebras and integrable systems, Proceedings of CAST First Academic Annual Meeting of Youths, Science Volume, Chinese Science and Technology Press, 1992, 7--14(in Chinese)


• W. X. Ma, On the complete integrability of nonlinearized Lax systems for the classical Boussinesq hierarchy, Acta Mathematicae Applicatae Sinica, Vol.9, No.1(1993), 92--96


• W. X. Ma, The unified structure of zero curvature representations of integrable hierarchies, Chinese Science Bulletin, Vol.38, No.24(1993), 2025--2031


• W. X. Ma, Hereditary symmetries and integrable systems for a class of Hamiltonian operators Applied Mathematics---A Journal of Chinese Universities, Vol.8, No.1(1993), 28--35(in Chinese) (MR 94c:35159)


• W. X. Ma, The algebraic structure of zero curvature representations and application to coupled KdV systems, Journal of Physics A: Mathematical and General, Vol.26(1993), 2573--2582 (MR 94i:58088)


• W. X. Ma, A simple scheme for generating nonisospectral flows from zero curvature representation, Physics Letters A, Vol.179(1993), 179--185 (MR 94f:58063)


• W. X. Ma, An exact solution to two dimensional Korteweg-de Vries-Burgers equation, Journal of Physics A: Mathematical and General, Vol.26(1993), L17--L20 (MR 93k:35235)


• W. X. Ma, A method of zero curvature representation for constructing symmetry algebras of integrable systems, Proceedings of the 21st International Conference on the Differential Geometry Methods in Theoretical Physics, World Scientific, 1993, 535--538


• W. X. Ma and D. T. Zhou, Solitary wave solutions to a generalized KdV equation, Acta Physica Sinica, Vol.42, No.11(1993), 1731--1734(in Chinese) (MR 95d:35154)


• W. X. Ma, Travelling wave solutions to a seventh order generalized KdV equation, Physics Letters A, Vol.180(1993), 221--224 (MR 94m:35268)


• W. X. Ma, Lax operator algebras and applications to integrable hierarchies, Proceedings of First Academic Annual Meeting of Chinese Postdoctors, Beijing University Press, 1993, 1261--1266


• W. X. Ma, A hierarchy of coupled Burgers systems possessing a hereditary structure, Journal of Physics A: Mathematical and General, Vol.26(1993), L1169--L1174 (MR 94k:35284)


• W. X. Ma, Exact solutions to the Tu system through Painlevé analysis, Journal of Fudan University (Natural Science), Vol.33, No.3(1994), 319--326 (MR 96c:35169)


• W. X. Ma, The Lie algebra structures of time-dependent symmetries of evolution equations, Acta Mathematicae Applicatae Sinica, Vol.17(1994), 388--392(in Chinese) (MR 97a:58168)


• W. X. Ma, Virasoro algebras of hierarchies of nonisospectral Lax operators, Journal of Systems Science and Mathematical Sciences, Vol.14, No.4(1994), 309--316(in Chinese) (MR 96d:58066)


• W. X. Ma, Lax representations of hierarchies of evolution equations with Lienard recursive structures, Acta Mathematica Scientia, Vol.14, No.4(1994), 409--418 (in Chinese) (MR 96b:35206)


• W. X. Ma and W. Strampp, An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems, Physics Letters A, Vol.185(1994), 277--286 (MR 95a:58059)


• W. X. Ma, New finite dimensional integrable systems by symmetry constraint of the KdV equations, Journal of the Physical Society of Japan, Vol.64(1995), 1085--1091 (MR 96a:35174)


• X. G. Geng and W. X. Ma, A generalized Kaup-Newell spectral problem, soliton equations and finite-dimensional integrable systems, Il Nuovo Cimento A, Vol.108(1995), 477--486 (MR 96m:35265)


• W. X. Ma, Symmetry constraint of MKdV equations by binary nonlinearization, Physica A, Vol.219(1995), 467--481 (MR 96f:35145)

1996-2000:

• W. X. Ma and B. Fuchssteiner, Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, International Journal of Non-Linear Mechanics, Vol.31(1996), 329--338 (MR 97e:76012)


• W. X. Ma and B. Fuchssteiner, Binary nonlinearization of Lax pairs, Proceedings of the First Workshop on Nonlinear Physics in Gallipoli, Italy, World Scientific, 1996, 217--224 (MR 98e:58099)


• W. X. Ma, B. Fuchssteiner and W. Oevel, A three-by-three matrix spectral problem for AKNS hierarchy and its binary nonlinearization, Physica A, Vol.233(1996), 331--354 (MR 97k:58082)


• W. X. Ma, Q. Ding, W. G. Zhang and B. Q. Lu, Binary nonlinearization of Lax pairs of Kaup-Newell soliton hierarchy, Il Nuovo Cimento B, Vol.111(1996), 1135--1149


• W. X. Ma and B. Fuchssteiner, The bi-Hamiltonian structures of the perturbation equations of KdV hierarchy, Physics Letters A, Vol.213(1996), 49--55 (MR 97a:58080)


• W. X. Ma and B. Fuchssteiner, Integrable theory of the perturbation equations, Chaos, Solitons & Fractals, Vol.7, No.8(1996), 1227--1250 (MR 97e:58113)


• W. X. Ma and Z. X. Zhou, Coupled integrable systems associated with a polynomial spectral problem and their Virasoro symmetry algebras, Progress of Theoretical Physics, Vol.96(1996), 449--457 (MR 97j:58064)


• W. X. Ma and K. S. Li, Virasoro symmetry algebra of Dirac soliton hierarchy, Inverse Problems, Vol.12(1996), L25--L31 (MR 97j:58135)


• W. X. Ma, Darboux transformations for a Lax integrable system in 2n-dimensions, Letters in Mathematical Physics, Vol.39(1997), 33--49 (MR 98e:58153)


• W. X. Ma, Problems and Solutions, no.10601, The American Mathematical Monthly, Vol.104(1997), 566


• W. X. Ma and G. F. Guo, Lax representations and zero curvature representations by Kronecker product, International Journal of Theoretical Physics, Vol.36(1997), 697--704 (MR 98m:58098)


• W. X. Ma, A note on symmetries and generalized W∞-algebra of the modified KP equation, Letters in Mathematical Physics, Vol.39(1997), 237--241 (MR 98h:58082)


• W. X. Ma, Binary nonlinearization for the Dirac systems, Chinese Annals of Mathematics, Series B, Vol.18B(1997), 79--88 (MR 98h:58081)


• W. X. Ma, R. K. Bullough, P. J. Caudrey and W. I. Fushchych, Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras, Journal of Physics A: Mathematical and General, Vol.30(1997), 5141--5149 (MR 98i:58119)


• W. X. Ma, R. K. Bullough and P. J. Caudrey, Graded symmetry algebras of time-dependent evolution equations and application to the modified KP equations, Journal of Nonlinear Mathematical Physics, Vol.4(1997), 293--309 (MR 98m:35006)


• W. X. Ma and D. T. Zhou, Explicit exact solutions to a generalized KdV equation, Acta Mathematica Scientia, Vol.17(Supp.)(1997), 168--174


• W. X. Ma, Extension of hereditary symmetry operators, Journal of Physics A: Mathematical and General, Vol.31(1998), 7279--7289 (MR 99f:58100)


• W. X. Ma, A class of coupled KdV systems and their bi-Hamiltonian formulation, Journal of Physics A: Mathematical and General, Vol.31(1998), 7585--7591 (MR 99j:58095)


• W. X. Ma and M. Pavlov, Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems, Physics Letters A, Vol.246(1998), 511--522


• R. G. Zhou and W. X. Ma, New classical and quantum integrable systems related to the MKdV integrable hierarchy, Journal of the Physical Society of Japan, Vol.67(1998), 4045--4050 (MR 2000c:37111)


• B. Fuchssteiner and W. X. Ma, An approach to master symmetries of lattice equations, in: Symmetries and Integrability of Difference Equations, London Math. Soc. Lecture Note Series 255, edited by P. A. Clarkson and F. W. Nijhoff (Cambridge University Press, Cambridge, 1999) 247--260 (MR 2000e:37104)


• W. X. Ma and B. Fuchssteiner, Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations, Journal of Mathematical Physics, Vol.40(1999), 2400--2418 (MR 2000c:37118) solv-int/9809009


• W. X. Ma, Comment on "Generalized W∞-symmetry algebra of the conditionally integrable nonlinear evolution equation", Journal of Mathematical Physics, Vol.40(1999), 3685--3690


• W. X. Ma and R. G. Zhou, On inverse recursion operator and tri-Hamiltonian formulation for a Kaup-Newell system of DNLS equations, Journal of Physics A: Mathematical and General, Vol.32(1999), L239--L242 (MR 2000f:37101)


• Y. B. Zeng and W. X. Ma, The construction of canonical separated variables for the binary constrained AKNS flow, Physica A, Vol.274(1999), 505--515


• W. X. Ma and R. G. Zhou, A coupled AKNS-Kaup-Newell soliton hierarchy, Journal of Mathematical Physics, Vol.40(1999), 4419--4428 (MR 2000d:37085)


• Y. B. Zeng and W. X. Ma, Families of quasi-bi-Hamiltonian systems and separability, Journal of Mathematical Physics, Vol.40(1999), 4452--4473 (MR 2000f:37108)


• W. X. Ma, X. B. Hu, S. M. Zhu and Y. T. Wu, Bäcklund transformation and its superposition principle of a Blaszak-Marciniak four-field lattice, Journal of Mathematical Physics, Vol.40(1999), 6071--6086 (MR 2000h:37125)


• Y. B. Zeng and W. X. Ma, Separation of variables for soliton equations via their binary constrained flows, Journal of Mathematical Physics, Vol.40(1999), 6526--6557 (MR 2001e:37093)


• W. G. Zhang and W. X. Ma, Explicit solitary-wave solutions to generalized Pochhammer-Chree equations, Applied Mathematics and Mechanics, Vol.20(1999), no.6, 666--674 (MR 2000i:35172)


• Y. S. Li and W. X. Ma, Binary nonlinearization of AKNS spectral problem under higher-order symmetry constraints, Chaos, Solitons & Fractals, Vol.11(2000), 697--710 (MR 2001a:37108)


• H. W. Tam, W. X. Ma, X. B. Hu and D. L. Wang, The Hirota-Satsuma coupled KdV equation and a coupled Ito system revisited, Journal of the Physical Society of Japan, Vol.69(2000), 45--52 (MR 2001c:35229)


• R. G. Zhou and W. X. Ma, The r-matrix structure of the restricted coupled AKNS-Kaup-Newell flow, Applied Mathematics Letters, Vol.13(2000), 131--135 (MR 2000m:37165)


• K. M. Tamizhmani and W. X. Ma, Master symmetries from Lax operators for certain lattice soliton hierarchies, Journal of the Physical Society of Japan, Vol.69(2000), 351--361 (MR 2002a:37111)


• W. X. Ma and X. G. Geng, New completely integrable Neumann systems related to the perturbation KdV hierarchy, Physics Letters B, Vol.475(2000), 56--62 (MR 2000m:37107)


• W. X. Ma, Integrable couplings of soliton equations by perturbations I. A general theory and application to the KdV hierarchy, Methods and Applications of Analysis, Vol.7(2000), no. 1, 21--56 (MR 2001k:37115)


• W. X. Ma and Y. S. Li, Do symmetry constraints nonlinearize spectral problems into Hamiltonian systems? Physics Letters A, Vol.268(2000), no.4-6, 352--359 (MR 2001b:37100)


• R. G. Zhou and W. X. Ma, Classical r-matrix structures of integrable mappings related to the Volterra lattice, Physics Letters A, Vol.269(2000), no.2-3, 103--111 (MR 2001d:37128)


• Y. B. Zeng, W. X. Ma and R. L. Lin, Integration of the soliton hierarchy with self-consistent sources, Journal of Mathematical Physics, Vol.41(2000), no.8, 5453--5489 (MR 2001c:37085)


• Y. S. Li and W. X. Ma, Hamiltonian structures of binary higher-order constrained flows associated with two 3 x 3 spectral problems, Physics Letters A, Vol.272(2000), no.4, 245--256 (MR 2001m:37140)


• Y. S. Li, W. X. Ma and J. E. Zhang, Darboux transformations of classical Boussinesq system and its new solutions, Physics Letters A, Vol.275(2000), 60--66 (MR 2002f:35112)


• X. G. Geng and W. X. Ma, A multipotential generalization of the nonlinear diffusion equation. Journal of the Physical Society of Japan, Vol.69(2000), no.4, 985--986 (MR 2001a:37102)


• W. X. Ma and R. G. Zhou, Liouville integrability of perturbation systems of finite-dimensional integrable Hamiltonian systems, Physics Letters A, Vol.276(2000), 73--78 (MR 2002b:70025)


• R. G. Zhou and W. X. Ma, Algebro-geometric solutions of the (2+1)-dimensional Gardner equation, Nuovo Cimento B, Vol.115(2000), 1419--1431 (MR 2002c:37116) )

2001-2005:

• W. X. Ma and S. M. Zhu, Non-symmetry constraints of the AKNS system yielding integrable Hamiltonian systems, Chaos, Solitons & Fractals, Vol.12(2001), 67--72 (MR 2001h:37142)


• Z. X. Zhou and W. X. Ma, Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints, Journal of the Physical Society of Japan, Vol.70(2001), 1241--1245


• W. X. Ma and R. G. Zhou, Nonlinearization of spectral problems of the perturbation KdV systems, Physica A, Vol.296(2001), 60--74 (MR 2002h:35227)


• Y. B. Zeng, W. X. Ma and Y. J. Shao, Two binary Darboux transformations for the KdV hierarchy with self-consistent sources, Journal of Mathematical Physics, Vol.42(2001), 2113--2128 (MR 2002b:37116)


• R. L. Lin, Y. B. Zeng and W. X. Ma, Solving the KdV hierarchy with self-consistent sources by inverse scattering method, Physica A, Vol.291(2001), 287--798 (MR 2002c:35231)


• W. X. Ma and R. G. Zhou, On the relationship between classical Gaudin models and BC-type Gaudin models, Journal of Physics A: Mathematical and General, Vol.34(2001), 867--880 (MR 2002d:82022)


• Z. X. Zhou, W. X. Ma and R. G. Zhou, Finite-dimensional integrable systems associated with the Davey-Stewartson I equation, Nonlinearity, Vol.14(2001), 701--717 (MR 2003a:37078)


• W. X. Ma and X. G. Geng, Bäcklund transformations of soliton systems from symmetry constraints, CRM Proceedings and Lecture Notes, Vol.29(2001), 313--323 (MR 2002m:37112)


• W. X. Ma, Binary Bargmann symmetry constraints of soliton equations, Nonlinear Analysis, Vol.47(2001), 5199--5211 (MR 2004d:37109)


• W. X. Ma and Z. X. Zhou, Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions, Journal of Mathematical Physics, Vol.42(2001), 4345--4382 (MR 2002k:37128)


• W. X. Ma and R. G. Zhou, Binary nonlinearization of spectral problems of the perturbation AKNS systems, Chaos, Solitons & Fractals, Vol.13(2002), 1451--1463 (MR 2003a:37097)


• W. X. Ma and R. G. Zhou, Adjoint symmetry constraints leading to binary nonlinearization, Journal of Nonlinear Mathematical Physics, Vol.9(2002), Supplement, 106--126 (MR 2004a:37086)


• K. Maruno and W. X. Ma, Bilinear forms of integrable lattices related to Toda and Lotka-Volterra lattices, Journal of Nonlinear Mathematical Physics, Vol.9(2002), Supplement, 127--139 (MR 2004a:37106)


• W. X. Ma, A bi-Hamiltonian formulation for triangular systems by perturbations, Journal of Mathematical Physics, Vol.43(2002), no. 3, 1408--1421 (MR 2002k:37129)


• X. B. Hu and W. X. Ma, Application of Hirota's bilinear formalism to the Toeplitz lattice--some special soliton-like solutions, Physics Letters A, Vol.293(2002), no. 3-4, 161--165 (MR 2003a:37110)


• M. Blaszak and W. X. Ma, New Liouville integrable noncanonical Hamiltonian systems from the AKNS spectral problem, Journal of Mathematical Physics, Vol.43(2002), no. 6, 3107--3123 (MR 2003g:37112)


• W. X. Ma and Y. B. Zeng, Binary constrained flows and separation of variables for soliton equations, Australian & New Zealand Industrial and Applied Mathematics Journal, Vol.44(2002), 129--139 (MR 2004c:37164) (ps file, pdf file)


• W. X. Ma, The theory of binary nonlinearization and its applications to soliton equations, Proceedings of the Third Asian Mathematical Conference (2000, Diliman), World Scientific, River Edge, NJ, 2002, 337--351 (MR 2003d:37112)


• R. L. Lin, W. X. Ma and Y. B. Zeng, Higher order potential expansion for the continuous limits of the Toda hierarchy, Journal of Physics A: Mathematical and General, Vol.35(2002), 4915--4928 (MR 2003h:37118)


• W. X. Ma, Complexiton solutions to the Korteweg-de Vries equation, Physics Letters A, Vol.301(2002), 35--44 (MR 2003h:35237)


• Y. S. Li and W. X. Ma, A nonconfocal involutive system and constrained flows associated with the MKdV- equation, Journal of Mathematical Physics, Vol.43(2002), 4950--4962 (MR 2003f:37119)


• W. X. Ma and R. G. Zhou, Adjoint symmetry constraints of multicomponent AKNS equations, Chinese Annals of Mathematics, Series B, Vol.23(2002), 373--384 (MR 2003h:37119)


• Y. B. Zeng, Y. J. Shao and W. X. Ma, Integral-Type Darboux Transformations for the mKdV hierarchy with self-consistent sources, Communications in Theoretical Physics, Vol.38(2002), 641--648


• C. R. Gilson, X. B. Hu, W. X. Ma and H. W. Tam, Two integrable differential-difference equations derived from the discrete BKP equation and their related equations, Physica D, Vol.175(2003), 177--184 (MR 2004a:35202)


• M. Blaszak and W. X. Ma, Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems, Journal of Geometry and Physics, Vol.47(2003), 21--42 (MR 2004k:37117)


• P. Gao, B. L. Guo and W. X. Ma, Persistent homoclinic orbits for perturbed nonlinear Schroeding equation with derivative term, Advances in Mathematics (China), Vol.32(2003), 253--256


• W. X. Ma, Enlarging spectral problems to construct integrable couplings of soliton equations, Physics Letters A, Vol.316(2003), 72--76 (MR 2004g:37102)


• W. X. Ma, Diversity of exact solutions to a restricted Boiti-Leon-Pempinelli dispersive long-wave system, Physics Letters A, Vol.319(2003), 325--333 (MR 2004i:76028)


• W. X. Ma, Soliton, positon and negaton solutions to a Schroedinger self-consistent source equation, Journal of the Physical Society of Japan, Vol.72(2003), 3017--3019


• W. X. Ma, Wronskians, Generalized Wronskians and solutions to the Korteweg-de Vries equation, Chaos, Solitons & Fractals, Vol.19(2004), 163--170 (MR 2004j:35251)


• W. X. Ma and X. X. Xu, Positive and negative hierarchies of integrable lattice models associated with a Hamiltonian pair, International Journal of Theoretical Physics, Vol.43(2004), 219--235 (MR 2006a:37068)


• K. Maruno, W. X. Ma and M. Oikawa, Generalized Casorati determinant and positon-negaton-type solutions of the Toda lattice equation, Journal of the Physical Society of Japan, Vol.73(2004), 831--837


• W. X. Ma and X. X. Xu, A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations, Journal of Physics A: Mathematical and General, Vol.37(2004), 1323--1336 (MR 2005a:37145)


• W. X. Ma and Y. You, Rational solutions of the Toda lattice equation in Casoratian form, Chaos, Solitons & Fractals, Vol.22(2004), 395--406 (MR 2005b:37178)


• W. X. Ma and K. Maruno, Complexiton solutions of the Toda lattice equation, Physica A, Vol.343(2004), 219--237 (MR 2005h:37181)


• W. X. Ma and Y. You, Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions, Transactions of the American Mathematical Society, Vol.357(2005), 1753--1778 (MR 2005k:37156)


• W. X. Ma, Integrable couplings of vector AKNS soliton equations, Journal of Mathematical Physics, Vol.46(2005), 033507, 19 pp. (MR 2005k:37155)


• W. X. Ma, Complexiton solutions of the Korteweg-de Vries equation with self-consistent sources, Chaos, Solitons & Fractals, Vol.26(2005), 1453--1458


• W. X. Ma and W. Strampp, Bilinear forms and Bäcklund transformations of the perturbation systems, Physics Letters A, Vol.341(2005), 441--449 (MR 2006d:37126)


• W. X. Ma, Complexiton solutions to integrable equations, Nonlinear Analysis, Vol. 63(2005), e2461--e2471


• W. X. Ma, Integrability, in: Encyclopedia of Nonlinear Science, ed. A. Scott, Taylor & Francis (2005), 250--253

2006-2010:

• W. X. Ma, X. X. Xu and Y. F. Zhang, Semi-direct sums of Lie algebras and continuous integrable couplings, Physics Letters A, Vol.351(2006), 125--130 (MR 2006i:37149)


• W. X. Ma, X. X. Xu and Y. F. Zhang, Semidirect sums of Lie algebras and discrete integrable couplings, Journal of Mathematical Physics, Vol.47(2006), 053501, 16 pp. (MR 2007e:37047)


• W. X. Ma and M. Chen, Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras, Journal of Physics A: Mathematical and General, Vol.39(2006), 10787--10801 (MR 2007g:37050)


• W. X. Ma and H. Y. Wu, Time-space integrable decompositions of nonlinear evolution equations, Journal of Mathematical Analysis and Applications, Vol.324(2006), 134--149 (MR 2007j:37103)


• W. X. Ma, Mixed rational-soliton solutions to the Toda lattice equation, Differential & Difference Equations and Applications, 711--720, Hindawi Publ. Corp., New York, 2006 (MR 2008a:37087)


• W. X. Ma, H. Y. Wu and J. S. He, Partial differential equations possessing Frobenius integrable decompositions, Physics Letters A, Vol.364(2007), 29--32 MR2288009 (2007k:35421)


• W. X. Ma and M. Chen, Do symmetry constraints yield exact solutions? Chaos, Solitons & Fractals, Vol.32(2007), 1513--1517 MR2286313 (2007h:35005)


• C. X. Li, W. X. Ma, X. J. Liu and Y. B. Zeng, Wronskian solutions of the Boussinesq equation--solitons, negatons, positons and complexitons, Inverse Problems, Vol.23(2007), 279--296 MR2302974 (2007m:37164)


• S. B. Damelin and W. X. Ma, Preface [Special issue: Topics in integrable systems], Journal of Computational and Applied Mathematics, Vol.202(2007), 1--2


• W. X. Ma and B. Shekhtman, A linear system arising from a polynomial problem and its applications, Chinese Annals of Mathematics, Series B, Vol.28(2007), 283--292


• W. X. Ma, A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order, Physics Letters A, Vol.367(2007), 473--477


• J. S. He, K. L. Tian, A. Foerster and W. X. Ma, Additional symmetries and string equation of the CKP hierarchy, Letters in Mathematical Physics, Vol.81(2007), 119--134


• W. X. Ma, A discrete variational identity on semi-direct sums of Lie algebras, Journal of Physics A: Mathematical and Theoretical, Vol.40(2007), 15055--15069


• W. X. Ma, A multi-component Lax integrable hierarchy with Hamiltonian structure, Pacific Journal of Applied Mathematics, Vol.1(2008), 69--75


• W. X. Ma, J. S. He and Z. Y. Qin, A supertrace identity and its applications to superintegrable systems, Journal of Mathematical Physics, Vol.49(2008), 033511, 13 pp.


• L. Luo, W. X. Ma and E. G. Fan, The algebraic structure of zero curvature representations associated with integrable couplings, International Journal of Modern Physics A, Vol.23(2008), 1309--1325


• W. X. Ma, An application of the Casoratian technique to the 2D Toda lattice equation, Modern Physics Letters B, Vol.22(2008), 1815--1825


• W. X. Ma, Multi-component bi-Hamiltonian Dirac integrable equations, Chaos, Solitons & Fractals, Vol.39(2009), 282--287


• W. X. Ma, C. X. Li and J. S. He, A second Wronskian formulation of the Boussinesq equation, Nonlinear Analysis: Theory, Methods & Applications, Vol.70(2009), 4245--4258


• L. Gao, W. X. Ma and W. Xu, Travelling wave and double-solitary-like solutions to two nonlinear evolution equations, Dynamics of Continuous, Discrete & Impulsive Systems, Series A: Mathematical Analysis, Vol.16(2009), Differential Equations and Dynamical Systems, suppl. S1, 10--14


• W. X. Ma, The Casoratian technique for integrable lattice equations, Dynamics of Continuous, Discrete & Impulsive Systems, Series A: Mathematical Analysis, Vol.16(2009), Differential Equations and Dynamical Systems, suppl. S1, 201--207


• W. X. Ma, R. G. Zhou and L. Gao, Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in (2+1) dimensions, Modern Physics Letters A, Vol.24(2009), 1677--1688


• W. X. Ma and L. Gao, Coupling integrable couplings, Modern Physics Letters B, Vol.23(2009), 1847--1860


• W. X. Ma and J.-H. Lee, A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation, Chaos, Solitons & Fractals, Vol.42(2009), 1356--1363


• W. X. Ma, X. Gu and L. Gao, A note on exact solutions to linear differential equations by the matrix exponential, Advances in Applied Mathematics and Mechanics, Vol.1(2009), 573--580


• W. X. Ma, Variational identities and applications to Hamiltonian structures of soliton equations, Nonlinear Analysis: Theory, Methods & Applications, Vol.71(2009), e1716--e1726 (pdf file, )


• L. Gao, W. X. Ma and W. Xu, Travelling wave solutions to Zufiria's higher-order Boussinesq type equations, Nonlinear Analysis: Theory, Methods & Applications, Vol.71(2009), e711-e724


• W. X. Ma and M. Chen, Direct search for exact solutions to the nonlinear Schrödinger equation, Applied Mathematics and Computation, Vol.215(2009), 2835--2842


• W. X. Ma, Wronskian solutions to integrable equations, Discrete and Continuous Dynamical Systems - Supplement 2009, 506--515


• W. X. Ma and B. Shekhtman, Do the chain rules for matrix functions hold without commutativity? Linear and Multilinear Algebra, Vol.58(2010), 79-87


• W. X. Ma and Y. Zhang, Component-trace identities for Hamiltonian structures, Applicable Analysis, Vol.89(2010), 457-472


• W. X. Ma, An extended Harry Dym hierarchy, Journal of Physics A: Mathematical and Theoretical, Vol.43(2010), 165202


• J. Yu, J. S. He, W. X. Ma and Y. Cheng, The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems, Chinese Annals of Mathematics, Series B, Vol.31(2010), no. 3, 361-372


• L. Gao, W. X. Ma and W. Xu, Frobenius integrable decompositions for ninth-order partial differential equations of specific polynomial type, Applied Mathematics and Computation, Vol.216(2010), 2728-2733


• W. X. Ma, Variational identities and Hamiltonian structures, in: Nonlinear and Modern Mathematical Physics, pp.1-27, edited by W. X. Ma, X. B. Hu and Q. P. Liu, AIP Conference Proceedings, Vol.1212 (American Institute of Physics, Melville, NY, 2010)


• W. X. Ma, Compatibility equations of the extended KP hierarchy, in: Nonlinear and Modern Mathematical Physics, pp.94-105, edited by W. X. Ma, X. B. Hu and Q. P. Liu, AIP Conference Proceedings, Vol.1212 (American Institute of Physics, Melville, NY, 2010)


• W. X. Ma, An extended noncommutative KP hierarchy, Journal of Mathematical Physics, Vol.51(2010), 073505


• W. X. Ma, T. W. Huang and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application, Physica Scripta, Vol.82(2010), 065003  (Most cited paper)


• Z. Wang and W. X. Ma, Discrete Jacobi sub-equation method for nonlinear differential-difference equations, Mathematical Methods in the Applied Sciences, Vol.33(2010), no. 12, 1463-1472


• W. X. Ma and Z. N. Zhu, Constructing nonlinear discrete integrable Hamiltonian couplings, Computers and Mathematics with Applications, Vol.60 (2010), 2601-2608

2011-2015:

• W. X. Ma, Commutativity of the extended KP flows, Communications in Nonlinear Science and Numerical Simulation, Vol.16(2011), 722-730


• W. X. Ma, Comment on the 3+1 dimensional Kadomtsev-Petviashvili equations, Communications in Nonlinear Science and Numerical Simulation, Vol.16(2011), 2663-2666


• W. X. Ma and E. G. Fan, Linear superposition principle applying to Hirota bilinear equations, Computers and Mathematics with Applications, Vol.61(2011), 950-959


• W. X. Ma, Nonlinear continuous integrable Hamiltonian couplings, Applied Mathematics and Computation, Vol.217(2011), 7238-7244


• W. X. Ma and A. Pekcan, Uniqueness of the Kadomtsev-Petviashvili and Boussinesq equations, Zeitschrift fr Naturforschung A, Vol.66(2011), 377-382


• Y. N. Tang, W. X. Ma, W. Xu and L. Gao, Wronskian determinant solutions of the (3 + 1)-dimensional Jimbo-Miwa equation, Applied Mathematics and Computation, Vol.217(2011), 8722-8730


• W. X. Ma, A. Abdeljabbar and M. G. Asaad, Wronskian and Grammian solutions to a (3+1)-dimensional generalized KP equation, Applied Mathematics and Computation, Vol.217(2011), 10016-10023


• L. Luo, W. X. Ma and E. G. Fan, An algebraic structure of zero curvature representations associated with coupled integrable couplings and applications to τ-symmetry algebras, International Journal of Modern Physics B, Vol.25(2011), 3237-3252


• W. X. Ma, Combined Wronskian solutions to the 2D Toda molecule equation, Physics Letters A, Vol.375(2011), 3931-3935


• M. E. H. Ismail and W. X. Ma, Equations of motion for zeros of orthogonal polynomials related to the Toda lattices, Arab Journal of Mathematical Sciences, Vol.17(2011), 1-10


• R. G. Zhou, W. X. Ma and J. L. Wang, Integrable deformations of binary constrained soliton flows, Chinese Annals of Mathematics, Series A, Vol.32(2011), 161-172; translation in Chinese Journal of Contemporary Mathematics, Vol.32(2011), 137-148


• W. X. Ma, Generalized bilinear differential equations, Studies in Nonlinear Sciences, Vol.2(2011), 140-144


• Y. N. Tang, W. X. Ma, W. Xu and L. Gao, Integrable coupling hierarchy and Hamiltonian structure for a matrix spectral problem with arbitrary-order, Communications in Nonlinear Science and Numerical Simulation, Vol.17(2012), 585-592


• M. G. Asaad and W. X. Ma, Pfaffian solutions to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation and its modified counterpart, Applied Mathematics and Computation, Vol.218(2012), 5524-5542


• W. X. Ma, Y. Zhang, Y. N. Tang and J. Y. Tu, Hirota bilinear equations with linear subspaces of solutions, Applied Mathematics and Computation, Vol.218(2012), 7174-7183


• W. X. Ma, Loop algebras and bi-integrable couplings, Chinese Annuals of Mathematics Series B, Vol.33(2012), 207-224


• Y. F. Zhang and W. X. Ma, Lie algebraic approach to nonlinear integrable couplings of evolution type, Journal of Applied Nonlinear Dynamics, Vol.1(2012), 1-28


• W. X. Ma and A. Abdeljabbar, A bilinear Bäcklund transformation of a (3+1)-dimensional generalized KP equation, Applied Mathematics Letters, Vol.12(2012), 1500-1504


• W. X. Ma, A refined invariant subspace method and applications to evolution equations, Science China Mathematics, Vol.55(2012), 1796-1778


• W. X. Ma and Y. P. Liu, Invariant subspaces and exact solutions of a class of dispersive evolution equations, Communications in Nonlinear Science and Numerical Simulation, Vol.17(2012), 3795-3801


• W. X. Ma and Z. N. Zhu, Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm, Applied Mathematics and Computation, Vol.218(2012), 11871-11879


• Z. Y. Qin, G. Mu and W. X. Ma, Painlevé integrability and complexiton-like solutions of a coupled Higgs model, International Journal of Theoretical Physics, Vol.51(2012), 999-1006


• Y. N. Tang, J. Y. Tu and W. X. Ma, Two new Wronskian conditions for the (3+1)-dimensional Jimbo-Miwa equation, Applied Mathematics and Computation, Vol.218(2012), 10050-100556


• Y. Zhang, Y. C. You, W. X. Ma and H. Q. Zhao, Resonance of solitons in a coupled higher-order Ito equation, Journal of Mathematical Analysis and Applications, Vol.394(2012), 121-128


• M. G. Asaad and W. X. Ma, Extended Gram-type determinant, wave and rational solutions to two (3+1)-dimensional nonlinear evolution equations, Applied Mathematics and Computation, Vol.219(2012), 213-225


• Abdeljabbar, W. X. Ma and A. Yildirim, Determinant solutions to a (3+1)-dimensional generalized KP equation with variable coefficients, Chinese Annals of Mathematics, Series B, Vol.33(2012), 641-650 121-128


• W. X. Ma, J. H. Meng and H. Q. Zhang, Integrable couplings, variational identities and Hamiltonian formulations, Global Journal of Mathematical Sciences, Vol.1(2012), 1-17


• Z. Y. Qin, W. X. Ma and H. C. Ma, Painlevé integrability of coupled variable coefficient higher-order nonlinear Schrödinger equations with free parameters, Chinese Annals of Mathematics, Series A, Vol.33(2012), 229-236


• H. T. Chen, S. H. Yang and W. X. Ma, Double sub-equation method for complexiton solutions of nonlinear partial differential equations, Applied Mathematics and Computation, Vol.219(2013), 4775-4781


• W. X. Ma, Bilinear equations, Bell polynomials and linear superposition principle, Journal of Physics: Conference Series, Vol.411(2013), 012021, pp. 11


• W. X. Ma and T. C. Xia, Pfaffianized systems for a generalized Kadomtsev-Petviashvili equation, Physica Scripta, Vol.87(2013), 055003, pp. 8


• W. X. Ma, A soliton hierarchy associated with so(3,R), Applied Mathematics and Computation, Vol.220(2013), 117-122


• W. X. Ma, J. H. Meng and H. Q. Zhang, Tri-integrable couplings by matrix loop algebras, International Journal of Nonlinear Sciences and Numerical Simulation, Vol.14(2013), 377-388


• J. H. Meng and W. X. Ma, Non-semisimple Lie algebras of block matrices and applications to bi-integrable couplings, Advances in Applied Mathematics and Mechanics, Vol.5(2013), 652-670


• W. X. Ma, H. Q. Zhang and J. H. Meng, A block matrix loop algebra and bi-integrable couplings of the Dirac equations, East Asian Journal on Applied Mathematics, Vol.3(2013), 171-189


• J. H. Meng and W. X. Ma, Hamiltonian tri-integrable couplings of the AKNS hierarchy, Communications in Theoretical Physics, Vol.59(2013), 385-392


• W. X. Ma, Bilinear equations and resonant solutions characterized by Bell polynomials, Reports on Mathematical Physics, Vol.72(2013), 41-56


• W. X. Ma, Trilinear equations, Bell polynomials, and resonant solutions, Frontiers of Mathematics in China, Vol.8(2013), 1139-1156


• H. C. Zheng, W. X. Ma and X. Gu, Hirota bilinear equations with linear subspaces of hyperbolic and trigonometric function solutions, Applied Mathematics and Computation, Vol.220(2013), 226-234


• W. X. Ma, J. H. Meng and B. Shekhtman, Tri-integrable couplings of the KdV hierarchy associated with a non-semisimple Lie algebra, Global Journal of Mathematical Sciences, Vol.2(2013), 9-19


• W. X. Ma, Lie algebra structures associated with zero curvature equations and generalized zero curvature equations, British Journal of Applied Science & Technology, Vol.3(2013), 1336-1344


• W. X. Ma, A spectral problem based on so(3,R) and its associated commuting soliton equations, Journal of Mathematical Physics, Vol.54(2013), 103509, pp. 8


• W. X. Ma, Integrable couplings and matrix loop algebras, in: Nonlinear and Modern Mathematical Physics, pp.105-122, edited by W. X. Ma and D. Kaup, AIP Conference Proceedings, Vol.1562 (American Institute of Physics, Melville, NY, 2013)


• S. W. Liu and W. X. Ma, The string equation and the tau-function Witt constraints for the discrete Kadomtsev-Petviashvili hierarchy, Journal of Mathematical Physics, Vol.54(2013), 103513, pp. 14


• W. G. Rui, W. X. Ma, C. M. Khalique and Z. N. Zhu, Study of integrability and exact solutions for nonlinear evolution equations, Abstract and Applied Analysis, Vol.2014(2014), Article ID 373745, pp3


• H. H. Dong, W. X. Ma, Y. F. Zhang and T. T. Chen, Integrable couplings: generation, Hamiltonian structures, conservation laws, and applications, Abstract and Applied Analysis, Vol.2014(2014), Article ID 356350, pp2


• H. Q. Zhang and W. X. Ma, Extended transformed rational function method and applications to complexiton solutions, Applied Mathematics and Computation, Vol.230(2014), 509-515


• W. X. Ma, S. Manukure and H. C. Zheng, A counterpart of the Wadati-Konno-Ichikawa soliton hierarchy associated with so(3,R), Zeitschrift für Naturforschung A, Vol.69(2014), 411-419


• Y. J. Ye, W. X. Ma, S. F. Shen and D. D. Zhang, A class of third-order nonlinear evolution equations admitting invariant subspaces and associated reductions, Journal of Nonlinear Mathematical Physics, Vol.21(2014), no. 1, 132-148


• W. X. Ma, An integrable counterpart of the D-AKNS soliton hierarchy from so(3,R), Physics Letters A, Vol.378(2014), no. 24-25, 1717-1720


• S. Manukure and W. X. Ma, Bi-integrable couplings of a new soliton hierarchy associated with a non-semisimple Lie algebra, Applied Mathematics and Computation, Vol.245(2014), 44-52


• W. X. Ma, C. G. Shi, E. A. Appiah, C. X. Li and S. F. Shen, An integrable generalization of the Kaup-Newell soliton hierarchy, Physica Scripta, Vol.89(2014), 065203, pp8


• G. Shi, W. X. Ma and M. McAnally, Integrable counterparts of the D-Kaup-Newell soliton hierarchy, Applied Mathematics and Computation, Vol.248(2014), 463-469


• W. X. Ma, T. C. Xia and Z. N. Zhu, A generalization of the Wadati-Konno-Ichikawa soliton hierarchy and its Liouville integrability, International Journal of Nonlinear Sciences and Numerical Simulation, Vol.15(2014), no. 6, 397-404


• W. X. Ma, S. F. Shen, S. M. Yu, H. Q. Zhang and W. Y. Zhang, An integrable SO(3,R)-counterpart of the Heisenberg soliton hierarchy, Reports on Mathematical Physics, Vol.74(2014), no. 3, 283-299


• W. Y. Zhang and W. X. Ma, An so(3,R) counterpart of the Dirac soliton hierarchy and its bi-integrable couplings, International Journal of Theoretical Physics, Vol.53(2014), 4211-4222


• S. Manukure, W. X. Ma and E. Appiah, A tri-Hamiltonian formulation of a new soliton hierarchy associated with so(3,R), Applied Mathematics Letters, Vol.39(2015), 28-30


• H. Y. Zhu, S. M. Yu, S. F. Shen and W. X. Ma, New integrable sl(2,R)-generalization of the classical Wadati-Konno-Ichikawa hierarchy, Communications in Nonlinear Science and Numerical Simulation, Vol.22(2015), no. 1-3, 1341-1349


• S. F. Shen, L. Y. Jiang, Y. Y. Jin and W. X. Ma, New soliton hierarchies associated with the Lie algebra so(3,R) and their bi-Hamiltonian structures, Reports on Mathematical Physics, Vol.75(2015), no. 1, 113-133


• Y. Zhang and W. X. Ma, Rational solutions to a KdV-like equation, Applied Mathematics and Computation, Vol.256(2015), 252-256


• Y. F. Zhang and W. X. Ma, A study on rational solutions to a KP-like equation, Zeitschrift für Naturforschung A, Vol.70(2015), 263-268


• S. M. Yu, Y. Q. Yao, S. F. Shen and W. X. Ma, Bi-integrable couplings of a Kaup-Newell type soliton hierarchy and their bi-Hamiltonian structures, Communications in Nonlinear Science and Numerical Simulation, Vol.23(2015), 366-377


• L. Y. Jiang, Y. Y. Jin, W. X. Ma, S. F. Shen and H. Y. Zhu, Novel soliton hierarchies of Levi type and their bi-Hamiltonian structures, Communications in Nonlinear Science and Numerical Simulation, Vol.23(2015), 388-396


• G. Shi, B. Z. Zhao and W. X. Ma, Exact rational solutions to a Boussinesq-like equation in (1+1)-dimensions, Applied Mathematics Letters, Vol.48(2015), 170-176


• Y. N. Tang, L. Wang and W. X. Ma, Integrable couplings, bi-integrable couplings and their Hamiltonian structures of the Giachetti-Johnson soliton hierarchy, Mathematical Methods in the Applied Sciences, Vol.38(2015), 2305-2315


• S. Manukure and W. X. Ma, A soliton hierarchy associated with a new spectral problem and its Hamiltonian structure, Journal of Mathematical Physics, Vol.56(2015), 021502, 7 pp.


• S. Manukure and W. X. Ma, An integrable extension of a soliton hierarchy associated with so(3,R) and its bi-Hamiltonian formulation, Journal of Mathematical Physics, Vol.56(2015), 111505, 8 pp.


• S. F. Shen, C. X. Li, Y. Y. Jin and S. M. Yu, Multi-component integrable couplings for the Ablowitz-Kaup-Newell-Segur and Volterra hierarchies, Mathematical Methods in the Applied Sciences, Vol.38(2015), 4345-4356


• W. X. Ma, Conservation laws of discrete evolution equations by symmetries and adjoint symmetries, Symmetry, Vol.7(2015), 714-725


• X. Lü, W. X. Ma and C. M. Khalique, A direct bilinear Bäcklund transformation of a (2+1)-dimensional Korteweg-de Vries-like model, Applied Mathematics Letters, Vol.50(2015), 37-42


• W. X. Ma, Lump solutions to the Kadomtsev-Petviashvili equation, Physics Letters A, Vol.379(2015), 1975-1978


• X. Lü, W. X. Ma, J. Yu, F. H. Lin and and C. M. Khalique, Envelope bright- and dark-soliton solutions for the Gerdjikov-Ivanov model, i>Nonlinear Dynamics, Vol.82(2015), 1211-1220

2016-2020:

• X. Lü, W. X. Ma, J. Yu and C. M. Khalique, Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrödinger equation, Communications in Nonlinear Science and Numerical Simulation, Vol.31(2016), 40-46


• W. X. Ma, J. H. Meng and M. S. Zhang, Nonlinear bi-integrable couplings with Hamiltonian structures, Mathematics and Computers in Simulation, Vol.127(2016), 166-177


• W. X. Ma, Z. Y. Qin and X. Lü, Lump solutions to dimensionally reduced p-gKP and p-gBKP equations, Nonlinear Dynamics, Vol.84(2016), 923-931


• X. Lü, W. X. Ma, S. T. Chen and C. M. Khalique, A note on rational solutions to a Hirota-Satsuma-like equation, Applied Mathematics Letters, Vol.58(2016), 13-18


• Ö. Ünsal and W. X. Ma, Linear superposition principle of hyperbolic and trigonometric function solutions to generalized bilinear equations, Computers and Mathematics with Applications, Vol.71(2016), 1242-1247


• X. Lü, W. X. Ma, Y. Zhou and C. M. Khalique, Rational solutions to an extended Kadomtsev-Petviashvili-like equation with symbolic computation, Computers and Mathematics with Applications, Vol.71(2016), 1560-1567


• Y. J. Ye, Z. H. Li, C. X. Li, S. F. Shen and W. X. Ma, A generalized Dirac soliton hierarchy and its bi-Hamiltonian structure, Applied Mathematics Letters, Vol.60(2016), 67-72


• Y. Q. Yao, S. F. Shen and W. X. Ma, A soliton hierarchy associated with a spectral problem of 2nd degree in a spectral parameter and its bi-Hamiltonian structure, Advances in Mathematical Physics, Vol.2016(2016), Article ID 3589704, 6 pages


• X. Lü and W. X. Ma, Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation, Nonlinear Dynamics, Vol.85(2016), 1217-1222


• W. X. Ma and Yuan Zhou, Reduced D-Kaup-Newell soliton hierarchies from sl(2,R) and so(3,R), International Journal of Geometric Methods in Modern Physics, Vol.13(2016), 1650105 (16 pages)


• X. Lu, S. T. Chen and W. X. Ma, Constructing lump solutions to a generalized Kadomtsev-Petviashvili-Boussinesq equation, Nonlinear Dynamics, Vol.86(2016), 523-534


• W. X. Ma, Y. Zhou and R. Dougherty, Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations, International Journal of Modern Physics B, Vol.30(2016), 1640018


• J. Y. Yang and W. X. Ma, Lump solutions to the BKP equation by symbolic computation, International Journal of Modern Physics B, Vol.30(2016), 1640028


• L. J. Zhang, C. M. Khalique and W. X. Ma, Classifying bilinear differential equations by linear superposition principle, International Journal of Modern Physics B, Vol.30(2016), 1640029


• W. X. Ma, Lump-type solutions to the (3+1)-dimensional Jimbo-Miwa equation, International Journal of Nonlinear Sciences and Numerical Simulation, Vol.17(2016), 355-359


• J. Y. Yang and W. X. Ma, Conservation laws of a perturbed Kaup-Newell equation, Modern Physics Letters B, Vol.30(2016), 1650381


• Y. J. Zhang, W. X. Ma and Ö. Ünsal, A novel kind of AKNS integrable couplings and their Hamiltonian structures, Turkish Journal of Mathematics, Vol.41(2017), no. 6, 1467-1476


• X. L. Yong, Y. J. Fan, Y. H. Huang, W. X. Ma, J. Tian, Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation, Modern Physics Letters B, Vol.31(2017), no. 30, 1750276, 14 pp.


• Y. Zhou and W. X. Ma, Complexiton solutions to soliton equations by the Hirota method, Journal of Mathematical Physics, Vol.58(2017), no. 10, 101511, 8 pp.


• H. Q. Zhao and W. X. Ma, Mixed lump-kink solutions to the KP equation, Computers & Mathematics with Applications, Vol.74(2017), no. 6, 1399-1405


• W. X. Ma, Trigonal curves and algebro-geometric solutions to soliton hierarchies I, Proceedings of the Royal Society A, Vol.473(2017), no. 2203, 20170232, 20 pp.


• W. X. Ma, Trigonal curves and algebro-geometric solutions to soliton hierarchies II, Proceedings of the Royal Society A, Vol.473(2017), no. 2203, 20170233, 20 pp.


• Ö. Ünsal, W. X. Ma and Y. J. Zhang, Multiple-wave solutions to generalized bilinear equations in terms of hyperbolic and trigonometric solutions, International Journal of Nonlinear Sciences and Numerical Simulation, Vol.18(2017), no. 5, 395-401


• L. N. Gao, Y. Y. Zi, Y. H. Yin, W. X. Ma and X. Lü, Bäcklund transformation, multiple wave solutions and lump solutions to a (3+1)-dimensional nonlinear evolution equation, Nonlinear Dynamics, Vol.89(2017), no. 3, 2233-2240


• H. Q. Zhang, Y. Wang, W. X. Ma, Binary Darboux transformation for the coupled Sasa-Satsuma equations, Chaos, Vol.27(2017), no. 7, 073102, 7 pp.


• J. Y. Yang and W. X. Ma, Abundant interaction solutions of the KP equation, Nonlinear Dynamics, Vol.89(2017), no. 2, 1539-1544


• J. B. Zhang and W. X. Ma, Mixed lump-kink solutions to the BKP equation, Computers & Mathematics with Applications, Vol.74(2017), no. 3, 591-596


• X. Gu, W. X. Ma and W. Y. Zhang, Two integrable Hamiltonian hierarchies in sl(2,R) and so(3,R) with three potentials, Journal of Mathematical Physics, Vol.58(2017), no. 5, 053512, 14 pp.


• H. Q. Zhang and W. X. Ma, Resonant multiple wave solutions for a (3+1)-dimensional nonlinear evolution equation by linear superposition principle, Computers & Mathematics with Applications, Vol.73(2017), no. 10, 2339-2343


• Y. Zhou and W. X. Ma, Applications of linear superposition principle to resonant solitons and complexitons, Computers & Mathematics with Applications, Vol.73(2017), no. 8, 1697-1706


• H. Q. Zhang and W. X. Ma, Lump solutions to the (2+1)-dimensional Sawada-Kotera equation, Nonlinear Dynamics, Vol.87(2017), no. 4, 2305-2310


• Y. J. Zhang, D. Zhao and W. X. Ma, A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations, Journal of Mathematical Physics, Vol.58(2017), no. 1, 013505, 19 pp.


• J. Y. Yang and W. X. Ma, Abundant lump-type solutions of the Jimbo-Miwa equation in (3+1)-dimensions, Computers & Mathematics with Applications, Vol.73(2017), no. 2, 220-225


• S. D. Zhu, S. F. Shen, Y. Y. Jin, C. X. Li and W. X. Ma, New soliton hierarchies associated with the real Lie algebra so(4,R), Mathematical Methods in the Applied Sciences, Vol.40(2017), no. 3, 680-698


• J. Yu, W. X. Ma, J. W. Han and S. T. Chen, An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation, Communications in Nonlinear Science and Numerical Simulation, Vol.43(2017), 151-157


• W. X. Ma and H. H. Dong, Modeling Riemann-Hilbert problems to get soliton solutions, Mathematical Modeling and Its Applications, Vol.6(2017), no. 3, 16-25


• W. X. Ma, Conservation laws by symmetries and adjoint symmetries, Discrete and Continuous Dynamical Systems Series S, 11 (2018), no. 4, 707-721


• W. X. Ma and Y. Zhou, Lump solutions to nonlinear partial differential equations via Hirota bilinear forms, Journal of Differential Equations, Vol.264(2018), no. 4, 2633-2659


• M. McAnally and W. X. Ma, An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy, Applied Mathematics and Computation, Vol.323(2018), 220-227


• W. X. Ma and Y. J. Zhang, Darboux transformations of integrable couplings and applications, Reviews in Mathematical Physics, Vol.30(2018), no. 2, 1850003, 26 pp.


• W. X. Ma, X. L. Yong and