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Traveling wave solutions for higher dimensional nonlinear evolution equations using the \((\frac{G'}{G})\)-expansion method. (English) Zbl 1228.35014

Summary: We construct traveling wave solutions involving parameters of nonlinear evolution equations 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 \((\frac{G'}{G})\)-expansion method, where \(G=G(\xi)\) satisfies a second order linear ordinary differential equation. For special parameter values solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.

MSC:

35A25 Other special methods applied to PDEs
35P05 General topics in linear spectral theory for PDEs
35C07 Traveling wave solutions
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