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The (G(')/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics
Faculty
Science
Year:
2009
Type of Publication:
Article
Pages:
Authors:
Gepreel, Khaled A, Zayed, E. M. E
DOI:
10.1063/1.3033750
Journal:
JOURNAL OF MATHEMATICAL PHYSICS AMER INST PHYSICS
Volume:
50
Research Area:
Physics
ISSN
ISI:000262969800032
Keywords :
functional analysis, Korteweg-de Vries equation, linear differential equations, nonlinear differential equations, rational functions, reaction-diffusion systems, solitons
Abstract:
I the present paper, we construct the traveling wave solutions involving parameters of the combined Korteweg-de Vries-modified Korteweg-de Vries equation, the reaction-diffusion equation, the compound KdV-Burgers equation, and the generalized shallow water wave equation by using a new approach, namely, the (G(')/G)-expansion method, where G=G(xi) satisfies a second order linear ordinary differential equation. When the parameters take special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions.
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