International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 379-384

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

Received 15 October 1999

Copyright © 2000 Kenneth L. Jones. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.