# 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. 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. , 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. , 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 $\tau$-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)
• 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.