Exact Solutions and Non-Traveling Wave Solutions of the (2+1)-Dimensional Boussinesq Equation

被引：1

作者：

Gao, Lihui ^{[1
]}

Guo, Chunxiao ^{[1
]}

Guo, Yanfeng ^{[2
,3
]}

Li, Donglong ^{[2
]}

机构：

[1] China Univ Min & Technol, Sch Sci, Beijing 100083, Peoples R China

[2] Guangxi Univ Sci & Technol, Sch Sci, Liuzhou 545006, Peoples R China

[3] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China

来源：

MATHEMATICS | 2022年 / 10卷 / 14期

基金：

中国国家自然科学基金;

关键词：

(2+1)-dimensional Boussinesq equation; homogeneous equilibrium principle; extended (G '/G) method; improved tanh function method; SYMBOLIC COMPUTATION;

D O I：

10.3390/math10142522

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By the extended (G'/G) method and the improved tanh function method, the exact solutions of the (2+1) dimensional Boussinesq equation are studied. Firstly, with the help of the solutions of the nonlinear ordinary differential equation, we obtain the new traveling wave exact solutions of the equation by the homogeneous equilibrium principle and the extended (G'/G) method. Secondly, by constructing the new ansatz solutions and applying the improved tanh function method, many non-traveling wave exact solutions of the equation are given. The solutions mainly include hyperbolic, trigonometric and rational functions, which reflect different types of solutions for nonlinear waves. Finally, we discuss the effects of these solutions on the formation of rogue waves according to the numerical simulation.

引用

页数：20

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