Solitons, Breathers, and Lump Solutions to the (2 + 1)‐Dimensional Generalized Calogero–Bogoyavlenskii–Schiff Equation

Abstract

In this paper, a generalized (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff equation is considered. Based on the Hirota bilinear method, three kinds of exact solutions, soliton solution, breather solutions, and lump solutions, are obtained. Breathers can be obtained by choosing suitable parameters on the 2-soliton solution, and lump solutions are constructed via the long wave limit method. Figures are given out to reveal the dynamic characteristics on the presented solutions. Results obtained in this work may be conducive to understanding the propagation of localized waves.

Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

“…Wang studied some local solitary wave solutions through choosing the long-wave limit approach [25]. Ma and Cheng studied the multisoliton solutions, one-breather and one-lump solution by using bilinear method [26]. Li obtain high-order lump by the directly methods [27].…”

Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

“…where a 3 a 6 ̸ = 0. Therefore, by comparing equation ( 6) and limiting conditions (10), we can write a type of quadratic function solutions of equation ( 5) Then, substituting quadratic function (11) into transformation (4), we can obtain…”

Dynamical analysis of diversity lump solutions to the (2+1)-dimensional dissipative Ablowitz–Kaup–Newell–Segure equation

“…In 2009, Villarroel et al [21] derived a class of localized solutions of a (2+1)-dimensional nonlinear Schrödinger equation and studied their dynamical properties. Ma et al [22][23][24][25][26][27] obtained a class of lump solutions of some nonlinear partial differential equations by the Hirota bilinear method. Wang et al [28] derived the lump solution when the period of complexiton solution went to infinite and investigated the dynamics of the lump solution of the Hirota bilinear equation in 2017.…”