A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation. (31st December 2012)

• Record Type: Journal Article
• Authors: Xiao, Yafeng; Xue, Haili; Zhang, Hongqing
• Other Names: Zhdanov Renat Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-12-31
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/896748
• Languages: English
• ISSNs: 1110-757X

Abstract

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.