[1] Ablowitz M J, Segur H. Solitons and the Inverse Scattering Transform. Philadelphia:SIAM, 1981
[2] Novikov S, Manakov S V, Pitaevskii, L P, Zakharov V E. Theory of Solitons-The Inverse Scattering Method. New York:Consultants Bureau, 1984
[3] Lax P D. Integrals of nonlinear equations of evolution and solitary waves. Commun Pure Appl Math, 1968, 21(5):467-490
[4] Blaszak M. Multi-Hamiltonian Theory of Dynamical Systems. Texts and Monographs in Physics, Berlin:Springer, 1998
[5] Miwa T, Jimbo M, Date E. Solitons:Differential Equations, Symmetries and Infinite Dimensional Algebras. Cambridge:Cambridge University Press, 2000
[6] Degasperis A. Resource letter sol-1:solitons. Am J Phys, 1998, 66(6):486-497
[7] Ma W X. Long-time asymptotics of a three-component coupled mKdV system. Mathematics, 2019, 7(7):
[8] Ma W X, Xu X X. A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations. J Phys A Math Gen, 2004, 37(4):1323-1336
[9] Tu G Z. A trace identity and its applications to the theory of discrete integrable systems. J Phys A Math Gen, 1990, 23(17):3903-3922
[10] Ma W X, Fuchssteiner B. Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations. J Math Phys, 1999, 40(5):2400-2418
[11] Abolowitz M J, Ladik J. F. Nonlinear differential-difference equations. J Math Phys, 1975, 16(3):598-603
[12] Abolowitz M J, Ladik J F. Nonlinear differential-difference equations and Fourier analysis. J Math Phys, 1976, 17(6):1011-1018
[13] Ma W X, Xu X X. Positive and negative hierarchies of integrable lattice models associated with a Hamiltonian pair. Int J Theoret Phys, 2004, 43(1):219-235
[14] Zeng Y B, Rauch-Wojciechowski S. Restricted flows of the Ablowitz-Ladik hierarchy and their continuous limits. J Phys A Math Gen, 1995, 28(1):113-134
[15] Liu X J, Zeng Y B. On the Ablowitz-Ladik equations with self-consistent sources. J Phys A Math Theor, 2007, 40(30):8765-8790
[16] Gerdzhikov V S, Ivanov M I. Hamiltonian structure of multicomponent nonlinear Schrödinger equations in difference form. Theoret Math Phys, 1982, 52(1):676-685
[17] Ablowitz M J, Prinari B, Trubatch A D. Discrete and Continuous Nonlinear Schrödinger Systems. Cambridge:Cambridge University Press, 2004
[18] Drinfel'd V G, Sokolov V V. Equations of Korteweg-de Vries type and simple Lie algebras. Soviet Math Dokl, 1982, 23(3):457-462
[19] Gerdjikov V S, Vilasi G, Yanovski A B. Integrable Hamiltonian Hierarchies:Spectral and Geometric Methods. Berlin:Springer-Verlag, 2008
[20] Ma W X, Xu X X, Zhang Y F. Semidirect sums of Lie algebras and discrete integrable couplings. J Math Phys, 2006, 47(5):053501
[21] Ma W X. A discrete variational identity on semi-direct sums of Lie algebras. J Phys A Math Theor, 2007, 40(50):15055-15069
[22] Geng X G. Darboux transformation of the discrete Ablowitz-Ladik eigenvalue problem. Acta Mathematica Scientia, 1989, 9(1):21-26
[23] Zhang D J, Ning T K, Bi J B, Chen D Y. New symmetries for the Ablowitz-Ladik hierarchies. Phys Lett A, 2006, 359(5):458-466
[24] Li Q, Chen D Y, Zhang J B, Chen S T. Solving the non-isopectral Ablowitz-Ladik hierarchy via the inverse scattering transform and reductions. Chaos Solitons Fractals, 2012, 45(12):1479-1485
[25] Li Q, Zhang J B, Chen D Y. The eigenfunctions and exact solutions of discrete mKdV hierarchy with self-consistent sources via the inverse scattering transform. Adv Appl Math Mech, 2015, 7(5):663-674
[26] Ma W X, Zhou Y. Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J Diff Eqn, 2018, 264(4):2633-2659
[27] Zhang Y, Dong H H, Zhang X E, Yang H W. Rational solutions and lump solutions to the generalized (3+1)-dimensional shallow water-like equation. Comput Math Appl, 2017, 73(2):246-252
[28] Chen S T, Ma W X. Lump solutions to a generalized Bogoyavlensky-Konopelchenko equation. Front Math China, 2018, 13(3):525-534
[29] Ma W X. Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs. J Geom Phys, 2018, 133:10-16
[30] Yong X L, Ma W X, Huang Y H, Liu Y. Lump solutions to the Kadomtsev-Petviashvili I equation with a self-consistent source. Comput Math Appl, 2018, 75(9):3414-3419
[31] Manukure S, Zhou Y, Ma W X. Lump solutions to a (2+1)-dimensional extended KP equation. Comput Math Appl, 2018, 75(7):2414-2419
[32] Ma W X. A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimensions. J Appl Anal Comput, 2019, 9(4):1319-1332
[33] Tang Y N, Tao S Q, Qing G. Lump solitons and the interaction phenomena of them for two classes of nonlinear evolution equations. Comput Math Appl, 2016, 72(9):2334-2342
[34] Zhao H Q, Ma W X. Mixed lump-kink solutions to the KP equation. Comput Math Appl, 2017, 74(6):1399-1405
[35] Zhang J B, Ma W X. Mixed lump-kink solutions to the BKP equation. Comput Math Appl, 2017, 74(3):591-596
[36] Kofane T C, Fokou M, Mohamadou A, Yomba E. Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation. Eur Phys J Plus, 2017, 132(11):465
[37] Yang J Y, Ma W X, Qin Z Y. Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation. Anal Math Phys, 2018, 8(3):427-436
[38] Ma W X, Yong Y L, Zhang H Q. Diversity of interaction solutions to the (2+1)-dimensional Ito equation. Comput Math Appl, 2018, 75(1):289-295.
[39] Ma W X. Interaction solutions to the Hirota-Satsuma-Ito equation in (2+1)-dimensions. Front Math China, 2019, 14(3):619-629
[40] Dorizzi B, Grammaticos B, Ramani A, Winternitz P. Are all the equations of the Kadomtsev Petviashvili hierarchy integrable? J Math Phys, 1986, 27(12):2848-2852
[41] Konopelchenko B, Strampp W. The AKNS hierarchy as symmetry constraint of the KP hierarchy. Inverse Probl, 1991, 7(2):L17-L24
[42] Yang Q Q, Zhao Q L, Li X Y. Explicit solutions and conservation laws for a new integrable lattice hierarchy. Complexity, 2019, 2019:5984356
[43] Dong H H, Zhang Y, Zhang X E. The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation. Commun Nonlinear Sci Numer Simulat, 2016, 36:354-365
[44] Liu Q S, Zhang R G, Yang L G, Song J. A new model equation for nonlinear Rossby waves and some of its solutions. Phys Lett A, 2019, 383(6):514-525
[45] Geng X G, Wu J P. Riemann-Hilbert approach and N-soliton solutions for a generalized Sasa-Satsuma equation. Wave Motion, 2016, 60:62-72
[46] Wang D S, Wang X L. Long-time asymptotics and the bright N-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach. Nonlinear Anal Real World Appl, 2018, 41:334-361
