BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR A GENERALIZED CAMASSA-HOLM EQUATION

Minzhi Wei; Xianbo Sun; Hongying Zhu

doi:10.11948/2018.1851

2018 Volume 8 Issue 6

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Minzhi Wei, Xianbo Sun, Hongying Zhu. BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR A GENERALIZED CAMASSA-HOLM EQUATION[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1851-1862. doi: 10.11948/2018.1851

Citation:

Minzhi Wei, Xianbo Sun, Hongying Zhu. BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR A GENERALIZED CAMASSA-HOLM EQUATION[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1851-1862. doi: 10.11948/2018.1851

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR A GENERALIZED CAMASSA-HOLM EQUATION

Department of Applied mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, China

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Abstract

Abstract

In this paper, the traveling wave solutions for a generalized CamassaHolm equation u_t-u_xxt=1/2 (p+1)(p+2)u^pu_x-1/2p(p-1)u^p-2u_x³-2pu^p-1u_xu_xx-u^pu_xxx are investigated. By using the bifurcation method of dynamical systems, three major results for this equation are highlighted. First, there are one or two singular straight lines in the two-dimensional system under some different conditions. Second, all the bifurcations of the generalized CamassaHolm equation are given for p either positive or negative integer. Third, we prove that the corresponding traveling wave system of this equation possesses peakon, smooth solitary wave solution, kink and anti-kink wave solution, and periodic wave solutions.
- Generalized Camassa-Holm equation /
- bifurcation theory /
- peakon /
- solitary wave solution /
- kink and anti-kink wave solutions
MSC: 35C08;37K40;74J35;35Q51

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References

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