%0 Journal Article
%T Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio
%A Liangwei He
%A Shuanghong Chen
%J American Journal of Computational Mathematics
%P 327-339
%@ 2161-1211
%D 2021
%I Scientific Research Publishing
%R 10.4236/ajcm.2021.114021
%X In this paper, we investigate the periodic wave solutions and solitary wave
solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation</span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10pt;font-family:&quot;\">by applying
Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function
solutions are obtained by choosing different </span><span style=\"font-size:10.0pt;font-family:&quot;\">coefficient</span><span style=\"font-size:10.0pt;font-family:&quot;\">s</span><span style=\"font-size:10pt;font-family:&quot;\"> <i>p</i>, <i>q</i> and <i>r</i> in the</span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10pt;font-family:&quot;\">elliptic
equation. Then these solutions are</span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10pt;font-family:&quot;\">coupled into an auxiliary equation</span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10pt;font-family:&quot;\">and
substituted into the (2+1)-dimensional KDV equation. As <span>a result,</span></span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10pt;font-family:&quot;\">a large
number of complex Jacobi elliptic function solutions are ob</span><span style=\"font-size:10pt;font-family:&quot;\">tained,
and many of them have not been found in other documents. As</span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10.0pt;font-family:&quot;\"><span></span></span><span style=\"font-size:10pt;font-family:&quot;\">, some complex solitary solutions are also obtained correspondingly.</span><span style=\"font-size:10pt;font-family:&quot;\"> </span><span style=\"font-size:10pt;font-family:&quot;\">These solutions that we
obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional
KDV equation.
%K Nonlinear Evolution Equations
%K Jacobi Elliptic Function
%K (2+1)-Dimensional KDV
%K Periodic Wave Solutions
%K Solitary Wave Solu-tions
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=114377