Smooth and non-smooth travelling wave solutions of generalized Degasperis-Procesi equation

Jianwei Shen; Wei Xu

doi:10.1016/j.amc.2006.05.029

Smooth and non-smooth travelling wave solutions of generalized Degasperis-Procesi equation

Jianwei Shen, Wei Xu

School of Mathematics and Statistics

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

6 Scopus citations

Abstract

The dynamical behavior and special exact solutions of the generalized Degasperis-Procesi equation u_t + c₀u_x - u_txx + auu_x = 3u_xu_xx + uu_xxx is analyzed by using bifurcation theory and the method of phase portraits analysis. As a result, the analytic expressions of peakon solutions, compacton solutions and periodic cusp wave solutions are obtained. And the condition under which peakon and compacton solutions appear are also given. In the meantime, the reason that solitary cusp wave and periodic cusp wave appear is given.

Original language	English
Pages (from-to)	1418-1429
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	182
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2006.05.029
State	Published - 15 Nov 2006

Keywords

Bifurcation theory
Compacton
Peakon
Periodic wave
Solitary waves

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10.1016/j.amc.2006.05.029

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title = "Smooth and non-smooth travelling wave solutions of generalized Degasperis-Procesi equation",

abstract = "The dynamical behavior and special exact solutions of the generalized Degasperis-Procesi equation ut + c0ux - utxx + auux = 3uxuxx + uuxxx is analyzed by using bifurcation theory and the method of phase portraits analysis. As a result, the analytic expressions of peakon solutions, compacton solutions and periodic cusp wave solutions are obtained. And the condition under which peakon and compacton solutions appear are also given. In the meantime, the reason that solitary cusp wave and periodic cusp wave appear is given.",

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author = "Jianwei Shen and Wei Xu",

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T1 - Smooth and non-smooth travelling wave solutions of generalized Degasperis-Procesi equation

AU - Shen, Jianwei

AU - Xu, Wei

PY - 2006/11/15

Y1 - 2006/11/15

N2 - The dynamical behavior and special exact solutions of the generalized Degasperis-Procesi equation ut + c0ux - utxx + auux = 3uxuxx + uuxxx is analyzed by using bifurcation theory and the method of phase portraits analysis. As a result, the analytic expressions of peakon solutions, compacton solutions and periodic cusp wave solutions are obtained. And the condition under which peakon and compacton solutions appear are also given. In the meantime, the reason that solitary cusp wave and periodic cusp wave appear is given.

AB - The dynamical behavior and special exact solutions of the generalized Degasperis-Procesi equation ut + c0ux - utxx + auux = 3uxuxx + uuxxx is analyzed by using bifurcation theory and the method of phase portraits analysis. As a result, the analytic expressions of peakon solutions, compacton solutions and periodic cusp wave solutions are obtained. And the condition under which peakon and compacton solutions appear are also given. In the meantime, the reason that solitary cusp wave and periodic cusp wave appear is given.

KW - Bifurcation theory

KW - Compacton

KW - Peakon

KW - Periodic wave

KW - Solitary waves

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DO - 10.1016/j.amc.2006.05.029

M3 - 文章

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VL - 182

SP - 1418

EP - 1429

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Smooth and non-smooth travelling wave solutions of generalized Degasperis-Procesi equation

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Keywords

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