The ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{G'}{G})$\end{document} -expansion method and its applications to some nonlinear evolution equations in the mathematical physics

In the present paper, we construct the traveling wave solutions involving parameters for some nonlinear evolution equations in the mathematical physics via the (2+1)-dimensional Painlevé integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Vesselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations by using a new approach, namely the ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{G'}{G})$\end{document} -expansion method, where G=G(ξ) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions.