Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation

Lijun Zhang; Li Qun Chen; Xuwen Huo

doi:10.1016/j.chaos.2005.08.202

Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation

Lijun Zhang
, Li Qun Chen^*
, Xuwen Huo

^*Corresponding author for this work

Zhejiang Sci-Tech University
Shanghai University

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equationm_t + c₀ u_x + um_x + 2 mu_x = - γ u_xxxwith m = u - α²u_xx, α ≠ 0, c₀, γ are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time.

Original language	English
Pages (from-to)	1238-1249
Number of pages	12
Journal	Chaos, Solitons and Fractals
Volume	30
Issue number	5
DOIs	https://doi.org/10.1016/j.chaos.2005.08.202
State	Published - Dec 2006
Externally published	Yes

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title = "Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation",

abstract = "By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equationmt + c0 ux + umx + 2 mux = - γ uxxxwith m = u - α2uxx, α ≠ 0, c0, γ are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time.",

author = "Lijun Zhang and Chen, \{Li Qun\} and Xuwen Huo",

year = "2006",

month = dec,

doi = "10.1016/j.chaos.2005.08.202",

language = "英语",

volume = "30",

pages = "1238--1249",

journal = "Chaos, Solitons and Fractals",

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T1 - Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation

AU - Zhang, Lijun

AU - Chen, Li Qun

AU - Huo, Xuwen

PY - 2006/12

Y1 - 2006/12

N2 - By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equationmt + c0 ux + umx + 2 mux = - γ uxxxwith m = u - α2uxx, α ≠ 0, c0, γ are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time.

AB - By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equationmt + c0 ux + umx + 2 mux = - γ uxxxwith m = u - α2uxx, α ≠ 0, c0, γ are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time.

UR - https://www.scopus.com/pages/publications/33745808306

U2 - 10.1016/j.chaos.2005.08.202

DO - 10.1016/j.chaos.2005.08.202

M3 - 文章

AN - SCOPUS:33745808306

SN - 0960-0779

VL - 30

SP - 1238

EP - 1249

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 5

ER -

Peakons and periodic cusp wave solutions in a generalized Camassa-Holm equation

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