A generalized F-expansion method with symbolic computation exactly solving Broer–Kaup equations

摘要

In this paper, a generalized F-expansion method is applied to construct exact solutions of the (2 + 1)-dimensional Broer–Kaup equations. As a result, many general exact non-travelling wave and coefficient function solutions are obtained including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions and trigonometric function solutions, each of which contains two arbitrary functions. Compared with most existing F-expansion methods, the proposed method gives new and more general exact solutions. More importantly, with the aid of symbolic computation, the method provides a powerful mathematical tool to solve a large many nonlinear partial differential equations.