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2012 A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation
Yafeng Xiao, Haili Xue, Hongqing Zhang
J. Appl. Math. 2012: 1-21 (2012). DOI: 10.1155/2012/896748

Abstract

With the aid of symbolic computation, a new extended Jacobi elliptic function expansion method is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function solutions of nonlinear partial differential equations. As an application of the method, we choose the generalized shallow water wave (GSWW) equation to illustrate the method. As a result, we can successfully obtain more new solutions. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.

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Yafeng Xiao. Haili Xue. Hongqing Zhang. "A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation." J. Appl. Math. 2012 1 - 21, 2012. https://doi.org/10.1155/2012/896748

Information

Published: 2012
First available in Project Euclid: 7 May 2014

zbMATH: 1308.76216
MathSciNet: MR3005229
Digital Object Identifier: 10.1155/2012/896748

Rights: Copyright © 2012 Hindawi

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