M-lump and hybrid solutions of a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation

Abstract In this paper, the N -soliton solutions of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation are obtained by means of the bilinear method. By applying the long wave limit to the N -solitons, the M -lump waves are constructed. The propagation orbits, velocities and the collisions among the lumps of the M -lump waves are analyzed. Three kinds of high-order hybrid solutions are presented, which contain the hybrid solution between lumps and solitons, a 1-lump and 1-breather, and a m -breather and n -soliton. The results are helpful to explain some nonlinear phenomena of the generalized shallow water wave model.

[1]  Yongli Sun,et al.  Lump solutions of the 2D Toda equation , 2020, Mathematical Methods in the Applied Sciences.

[2]  Zhonglong Zhao,et al.  Multiple lump solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation , 2019, Appl. Math. Lett..

[3]  Xiao-Yong Wen,et al.  The N-soliton solution and localized wave interaction solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito equation , 2019, Comput. Math. Appl..

[4]  Wen-Xiu Ma,et al.  Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation , 2020, Commun. Nonlinear Sci. Numer. Simul..

[5]  Tiecheng Xia,et al.  Dynamics of abundant solutions to the (3 + 1)-dimensional generalized Yu-Toda-Sasa-Fukuyama equation , 2020, Appl. Math. Lett..

[6]  J. Satsuma,et al.  Two‐dimensional lumps in nonlinear dispersive systems , 1979 .

[7]  Wenxiu Ma,et al.  A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equations via the linear superposition principle , 2020 .

[8]  Bo Han,et al.  Lump soliton, mixed lump stripe and periodic lump solutions of a (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation , 2017 .

[9]  W. Liu,et al.  High-order breathers, lumps, and semi-rational solutions to the (2 + 1)-dimensional Hirota–Satsuma–Ito equation , 2019, Physica Scripta.

[10]  B. Han,et al.  Lump solutions of a (3+1)-dimensional B-type KP equation and its dimensionally reduced equations , 2019 .

[11]  Biao Li,et al.  Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation , 2020, Physica Scripta.

[12]  Z. Dai,et al.  Dynamics of multi-breathers, N-solitons and M-lump solutions in the (2+1)-dimensional KdV equation , 2019, Nonlinear Dynamics.

[13]  Biao Li,et al.  Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation , 2019 .

[14]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for extended (3+1)-dimensional Jimbo-Miwa equations , 2017, Appl. Math. Lett..

[15]  B. Ghanbari,et al.  Resonant multi-soliton solutions to new (3+1)-dimensional Jimbo–Miwa equations by applying the linear superposition principle , 2019, Nonlinear Dynamics.

[16]  Yuan Zhou,et al.  Lump and lump-soliton solutions to the Hirota-Satsuma-Ito equation , 2019, Commun. Nonlinear Sci. Numer. Simul..

[17]  Yongjin Li,et al.  Bell polynomials and lump-type solutions to the Hirota–Satsuma–Ito equation under general and positive quadratic polynomial functions , 2020 .

[18]  J. Manafian,et al.  N-lump and interaction solutions of localized waves to the (2+1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation , 2020 .

[19]  H. An,et al.  General $${\varvec{M}}$$-lump, high-order breather and localized interaction solutions to the $$\varvec{2+1}$$-dimensional Sawada–Kotera equation , 2019, Nonlinear Dynamics.

[20]  Zhaqilao.  A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems , 2018, Comput. Math. Appl..

[21]  Jian‐Guo Liu,et al.  Multi-wave, breather wave, and interaction solutions of the Hirota–Satsuma–Ito equation , 2020 .

[22]  Yinping Liu,et al.  M-lump and interactive solutions to a (3 $${+}$$+ 1)-dimensional nonlinear system , 2018 .

[23]  Shou-Fu Tian,et al.  Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation , 2017, Appl. Math. Lett..

[24]  Yan Zhang,et al.  M-lump solutions to a (3+1)-dimensional nonlinear evolution equation , 2018, Comput. Math. Appl..

[25]  Ljudmila A. Bordag,et al.  Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction , 1977 .

[26]  Zhonglong Zhao,et al.  M-lump, high-order breather solutions and interaction dynamics of a generalized $$(2 + 1)$$-dimensional nonlinear wave equation , 2020, Nonlinear Dynamics.

[27]  Wenxiu Ma,et al.  Lump solutions to the Kadomtsev–Petviashvili equation , 2015 .