Exact Non-traveling Wave and Coefficient Function Solutions for (2+1)-Dimensional Dispersive Long Wave Equations

In this paper, a new generalized F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the (2+1)-dimensional dispersive long wave equations to illustrate the validity and advantages of the proposed method. As a result, many new and more general exact non-traveling 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. The arbitrary functions provide us with enough freedom to discuss the behaviors of solutions. As an illustrative example, new spatial structures of two solutions are shown. Compared with the most existing F-expansion methods, the new generalized F-expansion method gives not only more general exact solutions but also new formal exact solutions. The proposed method can also be applied to other nonlinear evolution equations in mathematical physics. c © Electronic Journal of Theoretical Physics. All rights reserved.