Zayed, E. M. E. Traveling wave solutions for higher dimensional nonlinear evolution equations using the \((\frac{G'}{G})\)-expansion method. (English) Zbl 1228.35014 J. Appl. Math. Inform. 28, No. 1-2, 383-395 (2010). 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. Cited in 30 Documents MSC: 35A25 Other special methods applied to PDEs 35P05 General topics in linear spectral theory for PDEs 35C07 Traveling wave solutions Keywords:YTSF equation; generalized shallow water equation; Kadomtsev-Petviashvili equation; modified KdV-Zakharov-Kuznetsev equation; Jimbo-Miwa equation PDFBibTeX XMLCite \textit{E. M. E. Zayed}, J. Appl. Math. Inform. 28, No. 1--2, 383--395 (2010; Zbl 1228.35014)