TRAVELING WAVE SOLUTIONS OF TWO TYPES OF GENERALIZED BREAKING SOLITON EQUATIONS

Li Wei; Yuqian Zhou; Qian Liu

doi:10.11948/20200373

2021 Volume 11 Issue 4

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Li Wei, Yuqian Zhou, Qian Liu. TRAVELING WAVE SOLUTIONS OF TWO TYPES OF GENERALIZED BREAKING SOLITON EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2151-2176. doi: 10.11948/20200373

Citation:

Li Wei, Yuqian Zhou, Qian Liu. TRAVELING WAVE SOLUTIONS OF TWO TYPES OF GENERALIZED BREAKING SOLITON EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2151-2176. doi: 10.11948/20200373

TRAVELING WAVE SOLUTIONS OF TWO TYPES OF GENERALIZED BREAKING SOLITON EQUATIONS

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) and China Postdoctoral Science Foundation (No. 2016M602663)

Abstract

Abstract

In this paper, the bifurcation theory of dynamical system is applied to study traveling waves of two types of generalized breaking soliton (GBS) equations which include many famous partial differential equation models. Without any parameter constraints, we investigate their traveling wave systems in detail from the geometric point of view. Due to the existence of a two dimensional invariant manifold, all bounded and unbounded orbits are identified and studied in different parameter bifurcation sets. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all possible single wave solutions of two types of GBS equations.
- GBS equations /
- traveling waves /
- bifurcation /
- dynamical system
MSC: 58F15, 58F17, 53C35

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References

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