International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 379-384
doi:10.1155/S0161171200004440
Three-dimensional Korteweg-de Vries equation and traveling wave solutions
Kenneth L. Jones
Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USA
Abstract
The three-dimensional power Korteweg-de Vries equation [ut+unux+uxxx]x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n=1 and n=2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.