Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa-Holm equation

Jianwei Shen; Wei Xu

doi:10.1016/j.chaos.2005.02.021

Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa-Holm equation

Jianwei Shen, Wei Xu

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

54 Scopus citations

Abstract

The dynamical behavior of travelling wave solutions in the Generalized Camassa-Holm equation u_t + 2ku_x - u_xxt + au^mu_x = 2u_xu_xx + uu_xxx is analyzed by using the bifurcation theory and the method of phase portraits analysis. The condition under which compactons and cusp waves appear are also given. In addition, the reason for solitary cusp wave and periodic cusp wave to exist is highlighted.

Original language	English
Pages (from-to)	1149-1162
Number of pages	14
Journal	Chaos, Solitons and Fractals
Volume	26
Issue number	4
DOIs	https://doi.org/10.1016/j.chaos.2005.02.021
State	Published - Nov 2005

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10.1016/j.chaos.2005.02.021

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title = "Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa-Holm equation",

abstract = "The dynamical behavior of travelling wave solutions in the Generalized Camassa-Holm equation ut + 2kux - uxxt + aumux = 2uxuxx + uuxxx is analyzed by using the bifurcation theory and the method of phase portraits analysis. The condition under which compactons and cusp waves appear are also given. In addition, the reason for solitary cusp wave and periodic cusp wave to exist is highlighted.",

author = "Jianwei Shen and Wei Xu",

year = "2005",

month = nov,

doi = "10.1016/j.chaos.2005.02.021",

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AU - Xu, Wei

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N2 - The dynamical behavior of travelling wave solutions in the Generalized Camassa-Holm equation ut + 2kux - uxxt + aumux = 2uxuxx + uuxxx is analyzed by using the bifurcation theory and the method of phase portraits analysis. The condition under which compactons and cusp waves appear are also given. In addition, the reason for solitary cusp wave and periodic cusp wave to exist is highlighted.

AB - The dynamical behavior of travelling wave solutions in the Generalized Camassa-Holm equation ut + 2kux - uxxt + aumux = 2uxuxx + uuxxx is analyzed by using the bifurcation theory and the method of phase portraits analysis. The condition under which compactons and cusp waves appear are also given. In addition, the reason for solitary cusp wave and periodic cusp wave to exist is highlighted.

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DO - 10.1016/j.chaos.2005.02.021

M3 - 文章

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JO - Chaos, Solitons and Fractals

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IS - 4

ER -

Bifurcations of smooth and non-smooth travelling wave solutions in the generalized Camassa-Holm equation

Abstract

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