Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio

Abstract

In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation by ap-plying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different coefficients p, q and r in the elliptic equation. Then these solutions are coupled into an auxiliary equation and substituted into the (2+1)-dimensional KDV equation. As a result, a large number of complex Jacobi elliptic function solutions are obtained, and many of them have not been found in other documents. As 1 m → , some complex solitary solutions are also obtained correspondingly. These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation.