A generalized G′G-expansion method and its application to the (2 + 1)-dimensional Broer–Kaup equations

In this paper, a generalized G′G-expansion method is used to seek more general exact solutions of the (2 + 1)-dimensional Broer–Kaup equations. As a result, non-travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. The proposed method is more powerful than Wang et al.’s method in [M.L. Wang, X.Z. Li, J.L. Zhang, The G′G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A 372 (2008) 417–423] and it can be used for many other nonlinear evolution equations in mathematical physics.