TRAVELING WAVES OF THE (3+1)-DIMENSIONAL KADOMTSEV-PETVIASHVILI-BOUSSINESQ EQUATION

Lan Wang; Yuqian Zhou; Qian Liu; Qiuyan Zhang

doi:10.11948/20190140

2020 Volume 10 Issue 1

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Lan Wang, Yuqian Zhou, Qian Liu, Qiuyan Zhang. TRAVELING WAVES OF THE (3+1)-DIMENSIONAL KADOMTSEV-PETVIASHVILI-BOUSSINESQ EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 267-281. doi: 10.11948/20190140

Citation:

Lan Wang, Yuqian Zhou, Qian Liu, Qiuyan Zhang. TRAVELING WAVES OF THE (3+1)-DIMENSIONAL KADOMTSEV-PETVIASHVILI-BOUSSINESQ EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 267-281. doi: 10.11948/20190140

TRAVELING WAVES OF THE (3+1)-DIMENSIONAL KADOMTSEV-PETVIASHVILI-BOUSSINESQ EQUATION

1.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China
2.
School of Computer Science and Technology, Southwest Minzu University, Chengdu 610041, Sichuan, China

Corresponding author: Email address: cs97zyq@aliyun.com(Y. Zhou)
Fund Project: This work is supported by the Natural Science Foundation of China (Nos. 11301043, 11701480), China Postdoctoral Science Foundation (No. 2016M602663), Innovative Research Team of the Education Department of Sichuan Province (No. 15TD0050)

Abstract

Abstract

In this paper, the bifurcation theory of dynamical system is applied to study the traveling waves of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq (KP-Boussinesq) equation. By transforming the traveling wave system of the KP-Boussinesq equation into a dynamical system in R³, we derive various parameter conditions which guarantee the existence of its bounded and unbounded orbits. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all possible traveling wave solutions of the (3+1)-dimensional KP-Boussines equation.
- KP-Boussinesq equation /
- traveling waves /
- bifurcation /
- dynamical system
MSC: 58F15, 58F17, 53C35

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