The Integrability and Several Localized Wave Solutions of a Generalized (2+1)-Dimensional Nonlinear Wave Equation

被引：0

作者：

Cui, Huilin ^{[1
]}

Feng, Yexuan ^{[1
]}

Zhao, Zhonglong ^{[1
]}

机构：

[1] North Univ China, Sch Math, Taiyuan 030051, Shanxi, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2025年 / 24卷 / 01期

基金：

中国国家自然科学基金;

关键词：

(2+1)-Dimensional nonlinear wave equation; Bell polynomials; Hirota's bilinear method; Localized wave solutions; DE-VRIES EQUATION; LUMP SOLUTIONS; BACKLUND-TRANSFORMATIONS; SYSTEM;

D O I：

10.1007/s12346-024-01176-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper mainly studies the integrability and localized wave solutions of a (2+1)-dimensional nonlinear wave equation. The bilinear form, B & auml;cklund transformation (BT), Lax pair and infinite conservation laws of this equation can be obtained by using Bell polynomials. The localized wave solutions including lump solutions, breather solutions and interaction solutions can be presented through Hirota's bilinear method and the ansatz method. In addition, based on mixed lump-stripe soliton solutions and mixed rogue wave-stripe soliton solutions, the fission and fusion phenomena among the lump, the single stripe soliton and the double stripe solitons are discovered. The dynamical behaviors of these localized wave solutions are analyzed by numerical simulations. These investigated solutions can enrich the study of theory for the nonlinear localized waves and are useful for the study on interaction behaviors of nonlinear waves in nonlinear optics, shallow water and oceanography.

引用

页数：28

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