Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation

Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation

By using the integral bifurcation method, we study the nonlinear K(m,n) equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodi...

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Main Authors: Xianbin Wu, Weiguo Rui, Xiaochun Hong
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/236875
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spelling doaj-f8cdd5991f0945808819edf2db86775a2020-11-25T00:56:04ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/236875236875Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) EquationXianbin Wu0Weiguo Rui1Xiaochun Hong2Junior College, Zhejiang Wanli University, Ningbo 315100, ChinaCollege of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaCollege of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, ChinaBy using the integral bifurcation method, we study the nonlinear K(m,n) equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions of K(n,n), K(2n−1,n), K(3n−2,n), K(4n−3,n), and K(m,1) equations are chosen to illustrate with the concrete features.http://dx.doi.org/10.1155/2012/236875
collection DOAJ
language English
format Article
sources DOAJ
author Xianbin Wu
Weiguo Rui
Xiaochun Hong
spellingShingle Xianbin Wu
Weiguo Rui
Xiaochun Hong
Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation
Journal of Applied Mathematics
author_facet Xianbin Wu
Weiguo Rui
Xiaochun Hong
author_sort Xianbin Wu
title Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation
title_short Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation
title_full Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation
title_fullStr Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation
title_full_unstemmed Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation
title_sort exact traveling wave solutions of explicit type, implicit type, and parametric type for k(m,n) equation
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description By using the integral bifurcation method, we study the nonlinear K(m,n) equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions of K(n,n), K(2n−1,n), K(3n−2,n), K(4n−3,n), and K(m,1) equations are chosen to illustrate with the concrete features.
url http://dx.doi.org/10.1155/2012/236875
work_keys_str_mv AT xianbinwu exacttravelingwavesolutionsofexplicittypeimplicittypeandparametrictypeforkmnequation
AT weiguorui exacttravelingwavesolutionsofexplicittypeimplicittypeandparametrictypeforkmnequation
AT xiaochunhong exacttravelingwavesolutionsofexplicittypeimplicittypeandparametrictypeforkmnequation
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