Single and multi-solitary wave solutions to a class of nonlinear evolution equations

In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate...

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Vydáno v:Journal of mathematical analysis and applications Ročník 343; číslo 1; s. 273 - 298
Hlavní autoři: Wang, Deng-Shan, Li, Hongbo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Inc 01.07.2008
Elsevier
Témata:
Bessel functions
Elliptic equation
Exact sciences and technology
Factorization technique
Global analysis, analysis on manifolds
Hirota's bilinear method
Mathematical analysis
Mathematics
Multi-solitary wave
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Painlevé analysis
Partial differential equations
Riccati equation
Sciences and techniques of general use
Special functions
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Travelling wave solution
Elliptic equation
Factorization technique
Hirota's bilinear method
Painlevé analysis
Riccati equation
Travelling wave solution
Multi-solitary wave
Bessel functions
Wave equation
Bessel function
Solitary wave
Evolution equation
Nonlinear problems
Camassa Holm equation
Travelling wave
Algorithm
Non linear equation
Direct method
Algorithm performance
Mathematical analysis
Application
Non linear wave
ISSN:0022-247X, 1096-0813
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Popis
Shrnutí:In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa–Holm equation, Kolmogorov–Petrovskii–Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the ( 2 + 1 ) -dimensional asymmetric version of the Nizhnik–Novikov–Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.01.039