Recent Publications

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) (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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, Available online 4 February 2016 (pdf file)
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 (pdf file)
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

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, Nonlinear Dynamics, Vol.82(2015), 1211-1220 (pdf file)
W. X. Ma, Lump solutions to the Kadomtsev-Petviashvili equation, Physics Letters A, Vol.379(2015), 1975-1978 (pdf file)
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 (pdf file)
W. X. Ma, Conservation laws of discrete evolution equations by symmetries and adjoint symmetries, Symmetry, Vol.7(2015), 714-725 (pdf file)
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
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. 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.
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
C. 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 (pdf file)
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 (pdf file)
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 (pdf file)
Y. F. Zhang and W. X. Ma, A study on rational solutions to a KP-like equation, Zeitschrift für Naturforschung A, Vol.70(2014), 263-268 (pdf file)
Y. Zhang and W. X. Ma, Rational solutions to a KdV-like equation, Applied Mathematics and Computation, Vol.256(2015), 252-256 (pdf file)
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
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. 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

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 (pdf file)
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 (pdf file)
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 (pdf file)
C. 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 (pdf file)
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 (pdf file)
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, An integrable counterpart of the D-AKNS soliton hierarchy from so(3,R), Physics Letters A Vol.378(2014), no. 24-25, 1717-1720 (pdf file)
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, S. Manukure and H. C. Zheng, A couterpart odf the Wadati-Konno-Ichikawa soliton hierarchy associated with so(3,R), Zeitschrift für Naturforschung A, Vol.69(2014), 411-419 (pdf file)
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
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
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

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 (pdf file)
W. X. Ma, Integrable couplings and matrix loop algebra, 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) (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
W. X. Ma, Trilinear equations, Bell polynomials, and resonant solutions, Frontiers of Mathematics in China, Vol.8(2013), 1139-1156 (pdf file)
W. X. Ma, Bilinear equations and resonant solutions characterized by Bell polynomials, Reports on Mathematical Physics, Vol.72(2013), 41-56
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, H. Q. Zhang and J. H. Meng, A block matrix loop algebra and bi-integrable couplings of the AKNS equations, East Asian Journal on Applied Mathematics, Vol.3(2013), 171-189 (pdf file)
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, 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 (pdf file)
W. X. Ma, A soliton hierarchy associated with so(3,R), Applied Mathematics and Computation, Vol.220(2013), 117-122 (pdf file)
W. X. Ma and T. C. Xia, Pfaffianized systems for a generalized Kadomtsev-Petviashvili equation, Physica Scripta, Vol.87(2013), 055003, pp. 8 (pdf file)
W. X. Ma, Bilinear equations, Bell polynomials and linear superposition principle, Journal of Physics: Conference Series, Vol.411(2013), 012021, pp. 11 (pdf file)
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

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
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 (pdf file)
A. 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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
W. X. Ma, A refined invariant subspace method and applications to evolution equations, Science China Mathematics, Vol.55(2012), 1796-1778 (pdf file)
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 (pdf file)
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 (pdf file)
W. X. Ma, Loop algebras and bi-integrable couplings, Chinese Annuals of Mathematics Series B, Vol.33(2012), 207-224 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)

W. X. Ma, Generalized bilinear differential equations, Studies in Nonlinear Sciences, Vol.2(2011), 140-144 (pdf file)
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
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 (pdf file)
W. X. Ma, Combined Wronskian solutions to the 2D Toda molecule equation, Physics Letters A, Vol.375(2011), 3931-3935 (pdf file)
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 (pdf file)
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 (pdf file)
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 (pdf file)
W. X. Ma and A. Pekcan, Uniqueness of the Kadomtsev-Petviashvili and Boussinesq equations, Zeitschrift für Naturforschung A, Vol.66(2011), 377-382 (pdf file)
W. X. Ma, Nonlinear continuous integrable Hamiltonian couplings, Applied Mathematics and Computation, Vol.217(2011), 7238-7244 (pdf file)
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 (pdf file)
W. X. Ma, Comment on the 3+1 dimensional Kadomtsev-Petviashvili equations, Communications in Nonlinear Science and Numerical Simulation, Vol.16(2011), 2663-2666 (pdf file)
W. X. Ma, Commutativity of the extended KP flows, Communications in Nonlinear Science and Numerical Simulation, Vol.16(2011), 722-730 (pdf file)

List of publications

Papers reviewed in Mathematical Reviews, American Mathematical Society

Papers stored in the e-print archive of nonlinear science at the Los Alamos National Laboratory, USA.

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