TITLE:
Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio
AUTHORS:
Liangwei He, Shuanghong Chen
KEYWORDS:
Nonlinear Evolution Equations, Jacobi Elliptic Function, (2+1)-Dimensional KDV, Periodic Wave Solutions, Solitary Wave Solu-tions
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.4,
December
31,
2021
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 applying
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 , 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.