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https://doi.org/10.1016/S0375-9601(01)00644-2

has been cited by the following article:

• 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.