Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation

Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation

We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x=3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton s...

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Main Authors: Jiangbo Zhou, Lixin Tian
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2009/249361
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spelling doaj-1ac57c815bbe4d97b85866539852bb5c2020-11-25T01:06:12ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472009-01-01200910.1155/2009/249361249361Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi EquationJiangbo Zhou0Lixin Tian1Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaNonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaWe employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x=3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.http://dx.doi.org/10.1155/2009/249361
collection DOAJ
language English
format Article
sources DOAJ
author Jiangbo Zhou
Lixin Tian
spellingShingle Jiangbo Zhou
Lixin Tian
Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
Mathematical Problems in Engineering
author_facet Jiangbo Zhou
Lixin Tian
author_sort Jiangbo Zhou
title Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
title_short Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
title_full Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
title_fullStr Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
title_full_unstemmed Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation
title_sort solitons, peakons, and periodic cuspons of a generalized degasperis-procesi equation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2009-01-01
description We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x=3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.
url http://dx.doi.org/10.1155/2009/249361
work_keys_str_mv AT jiangbozhou solitonspeakonsandperiodiccusponsofageneralizeddegasperisprocesiequation
AT lixintian solitonspeakonsandperiodiccusponsofageneralizeddegasperisprocesiequation
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