Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 50, Issue 1, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3033750
Keywords
functional analysis; Korteweg-de Vries equation; linear differential equations; nonlinear differential equations; rational functions; reaction-diffusion systems; solitons
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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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