Some applications of the G′G-expansion method to non-linear partial differential equations

摘要

In the present paper, we construct the traveling wave solutions involving parameters of the (2 + 1)-dimensional higher order Broer–Kaup equations, the (2 + 1)-dimensional breaking soliton equations, the (2 + 1)- dimensional asymmetric Nizhnik–Novikov–Vesselov equations and the (2 + 1)-dimensional BKP equations in terms of the hyperbolic functions, trigonometric functions and the rational functions by using a new approach, namely the G′G-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 the hyperbolic functions, the trigonometric functions and the rational functions.