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TRAVELING WAVE SOLUTIONS FOR HIGHER DIMENSIONAL NONLINEAR EVOLUTION EQUATIONS USING THE $(\frac{G- EXPANSION METHOD  

Zayed, E.M.E. (Mathematics Department, Faculty of Science, Zagazig University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 383-395 More about this Journal
Abstract
In the present paper, we construct the traveling wave solutions involving parameters of nonlinear evolution equations in the mathematical physics via the (3+1)- dimensional potential- YTSF equation, the (3+1)- dimensional generalized shallow water equation, the (3+1)- dimensional Kadomtsev- Petviashvili equation, the (3+1)- dimensional modified KdV-Zakharov- Kuznetsev equation and the (3+1)- dimensional Jimbo-Miwa equation by using a simple method which is called the ($\frac{G)- expansion method, where $G\;=\;G(\xi)$ satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.
Keywords
The ($\frac{G)- expansion method; traveling wave solutions; the potential- YTSF equation; the generalized shallow water equation; the Kadomtsev- Petviashvili equation; the modified KdV- Zakharov-Kuznetsev equation; the Jimbo-Miwa equation;
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