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A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation
- Source :
- Journal of Applied Mathematics, Vol 2012 (2012)
- Publication Year :
- 2012
- Publisher :
- Wiley, 2012.
-
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.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 1110757X and 16870042
- Volume :
- 2012
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.6a1cbf76eabb4c549924e4950ec3929b
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2012/896748