EXPLICIT SOLITON SOLUTIONS OF THE KAUP-KUPERSHMIDT EQUATION THROUGH THE DYNAMICAL SYSTEM APPROACH

Jibin Li; Zhijun Qiao

doi:10.11948/2011016

2011 Volume 1 Issue 2

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Jibin Li, Zhijun Qiao. EXPLICIT SOLITON SOLUTIONS OF THE KAUP-KUPERSHMIDT EQUATION THROUGH THE DYNAMICAL SYSTEM APPROACH[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 243-250. doi: 10.11948/2011016

Citation:

Jibin Li, Zhijun Qiao. EXPLICIT SOLITON SOLUTIONS OF THE KAUP-KUPERSHMIDT EQUATION THROUGH THE DYNAMICAL SYSTEM APPROACH[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 243-250. doi: 10.11948/2011016

EXPLICIT SOLITON SOLUTIONS OF THE KAUP-KUPERSHMIDT EQUATION THROUGH THE DYNAMICAL SYSTEM APPROACH

Jibin Li^1,2,
Zhijun Qiao³

1 Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China;
2 Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China;
3 Department of Mathematics, The University of Texas Pan-American, 1201 West University Drive, Edinburg, TX 78541, USA

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Abstract

Abstract

In this paper, we study the traveling wave solutions of the KaupKupershmidt (KK) equation through using the dynamical system approach, which is an integrable fifth-order wave equation. Based on Cosgrove's work[3] and the phase analysis method of dynamical systems, infinitely many soliton solutions are presented in an explicit form. To guarantee the existence of soliton solutions, we discuss the parameters range as well as geometrical explanation of soliton solutions.
- Soliton solution /
- quasi-periodic solution /
- periodic solution /
- KaupKupershmidt equation /
- homoclinic manifold /
- center manifold
MSC: 34C23;34C37;35Q55;37K45;58Z05;74J30

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References

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