An improved generalized F-expansion method and its application to the (2 + 1)-dimensional KdV equations

Abstract

An improved generalized F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2+1)-dimensional KdV equations to illustrate the validity and advantages of the proposed method. Many new and more general non-travelling wave solutions are obtained, including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, each of which contains two arbitrary functions.