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 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.
Share and Cite:
He, L. and Chen, S. (2021) Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio.
American Journal of Computational Mathematics,
11, 327-339. doi:
10.4236/ajcm.2021.114021.