Soliton-like solutions for a (2+1) -dimensional nonintegrable KdV equation and a variable-coefficient KdV equation

Abstract

Based on a Riccati equation and a symbolic computation system-Maple, a generalized Riccati equation expansion method is presented for constructing soliton-like solutions and periodic form solutions for some nonlinear evolution equations (NEEs) or NEEs with variable coefficients. Compared with most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and the generalized hyperbolic-function method, the proposed method is more powerful. We study a (2+1)-dimensional general nonintegrable KdV equation, a KdV equation with variable coefficients. As a result, rich new families of exact solutions, including the non-travelling wave's and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained. When setting the arbitrary functions in some solutions be equal to special constants or special functions, the solitary wave solutions can be recovered.