Application of the G′G-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations

By using the G′G-expansion proposed recently the travelling wave solutions involving parameters of the Broer-Kaup equations and the approximate long water wave equations are found out. The travelling wave solutions are expressed by three types of functions which are the hyperbolic functions, the trigonometric functions and the rational functions. When the parameters are taken as special values the solitary wave solutions are obtained.