A rational generalization of Fan’s method and its application to generalized shallow water wave equations

In this paper we employ a rational expansion to generalize Fan’s method for exact travelling wave solutions for nonlinear partial differential equations (PDEs). To verify the reliability of the proposed method, the generalized shallow water wave (GSWW) equation has been investigated as an example. K...

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Veröffentlicht in:	Applied mathematics and computation 2010-06, Vol.216 (7), p.1984-1995
Hauptverfasser:	Yang, Zonghang, Hon, Y.C.
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Exact solutions Fan’s method Mathematical analysis Mathematical models Mathematics Nonlinear differential equations Nonlinear equations Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Rational expansion Sciences and techniques of general use Shallow water The GSWW equation Traveling waves Travelling wave solution
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Beschreibung
Zusammenfassung:	In this paper we employ a rational expansion to generalize Fan’s method for exact travelling wave solutions for nonlinear partial differential equations (PDEs). To verify the reliability of the proposed method, the generalized shallow water wave (GSWW) equation has been investigated as an example. Kinds of new exact travelling wave solutions of a rational form have been obtained. This indicates that the proposed method provides a more general result for exact solution of nonlinear equations.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2010.03.029