| Volume 1, Number 2, 2011, Pages 243-250 DOI：10.11948/2011016 |
| Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach |
| Jibin Li,Zhijun Qiao |
| Keywords:Soliton solution, quasi-periodic solution, periodic solution, Kaup-Kupershmidtequation, homoclinic manifold, center manifold. |
| Abstract: |
| In this paper, we study the traveling wave solutions of the Kaup-Kupershmidt (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. |
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