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

数学与统计学院

Xuchang University
Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1418-1429
页数	12
期刊	Applied Mathematics and Computation
卷	182
期	2
DOI	https://doi.org/10.1016/j.amc.2006.05.029
出版状态	已出版 - 15 11月 2006

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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.",

keywords = "Bifurcation theory, Compacton, Peakon, Periodic wave, Solitary waves",

author = "Jianwei Shen and Wei Xu",

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language = "英语",

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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

UR - https://www.scopus.com/pages/publications/33751546314

U2 - 10.1016/j.amc.2006.05.029

DO - 10.1016/j.amc.2006.05.029

M3 - 文章

AN - SCOPUS:33751546314

SN - 0096-3003

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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