Lamé equation and asymptotic higher-order periodic solutions to nonlinear evolution equations
type: Item
instance of: scholarly article
title: Lamé equation and asymptotic higher-order periodic solutions to nonlinear evolution equations
zbMATH Open document ID: 1177.34073
author: Guanting Liu
published in: Applied Mathematics and Computation
publication date: 2009-06-24T00:00:00Z
review text: The perturbation method combined with an auxiliary Lamé equation is proposed to construct asymptotic higher-order periodic solutions to some nonlinear evolution equations. It is shown that the higher-order periodic solutions depend on the eigenfunctions of the Lamé equation; different eigenfunctions corresponds to different higher-order solutions. Since Jacobi elliptic functions are more general than the hyperbolic tangent and secant functions, the results of the paper give corresponding solitary or shock wave solutions. This method is also a computerizing method, which allows to perform complicated and tedious algebraic calculation by means of symbolic computation. The KdV equation, Klein-Gordon equation and Kadomtsev-Petviashvili equation are chosen to illustrate the effectiveness of the suggested method.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 5569571
zbMATH Keywords: Lame equation
zbMATH Keywords: asymptotic higher-order periodic solution
zbMATH Keywords: perturbation method
MaRDI profile type: Publication
full work available at URL: j.amc.2009.02.022
OpenAlex ID: W2001047444
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DOI: 10.1016/J.AMC.2009.02.022
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description: scientific article; zbMATH DE number 5569571