Bifurcations of smooth and nonsmooth traveling wave solutions in a generalized degasperis-procesi equation

Lijun Zhang; Li Qun Chen; Xuwen Huo

doi:10.1016/j.cam.2006.04.047

Bifurcations of smooth and nonsmooth traveling wave solutions in a generalized degasperis-procesi 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

14 Scopus citations

Abstract

In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equationu_t - u_xxt + 4 u^m u_x = 3 u_x u_xx + uu_xxx .The parameter condition under which peakons, compactons and periodic cusp wave solutions exist is given. The numerical simulation results show the consistence with the theoretical analysis at the same time.

Original language	English
Pages (from-to)	174-185
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	205
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2006.04.047
State	Published - 1 Aug 2007
Externally published	Yes

Keywords

Conpacton
GDP equation
Peakon
Periodic cusp wave
Phase portrait

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10.1016/j.cam.2006.04.047

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title = "Bifurcations of smooth and nonsmooth traveling wave solutions in a generalized degasperis-procesi equation",

abstract = "In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equationut - uxxt + 4 um ux = 3 ux uxx + uuxxx .The parameter condition under which peakons, compactons and periodic cusp wave solutions exist is given. The numerical simulation results show the consistence with the theoretical analysis at the same time.",

keywords = "Conpacton, GDP equation, Peakon, Periodic cusp wave, Phase portrait",

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

year = "2007",

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T1 - Bifurcations of smooth and nonsmooth traveling wave solutions in a generalized degasperis-procesi equation

AU - Zhang, Lijun

AU - Chen, Li Qun

AU - Huo, Xuwen

PY - 2007/8/1

Y1 - 2007/8/1

N2 - In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equationut - uxxt + 4 um ux = 3 ux uxx + uuxxx .The parameter condition under which peakons, compactons and periodic cusp wave solutions exist is given. The numerical simulation results show the consistence with the theoretical analysis at the same time.

AB - In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equationut - uxxt + 4 um ux = 3 ux uxx + uuxxx .The parameter condition under which peakons, compactons and periodic cusp wave solutions exist is given. The numerical simulation results show the consistence with the theoretical analysis at the same time.

KW - Conpacton

KW - GDP equation

KW - Peakon

KW - Periodic cusp wave

KW - Phase portrait

UR - https://www.scopus.com/pages/publications/34247343327

U2 - 10.1016/j.cam.2006.04.047

DO - 10.1016/j.cam.2006.04.047

M3 - 文章

AN - SCOPUS:34247343327

SN - 0377-0427

VL - 205

SP - 174

EP - 185

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Bifurcations of smooth and nonsmooth traveling wave solutions in a generalized degasperis-procesi equation

Abstract

Keywords

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