The improved fenced(frac(G^′, G))-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations

By introducing a new general ansätze, the improved fenced(frac(G^′, G))-expansion method is proposed to construct exact solutions of both Broer-Kaup equations and approximate long water wave equations. As a result, some new travelling wave solutions involving parameters, expressed by three types of functions which are the hyperbolic functions, the trigonometric functions and the rational functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions. The proposed method is straightforward, concise and effective, and can be applied to other nonlinear evolution equations in mathematical physics.