Three‐dimensional Korteweg‐de Vries equation and traveling wave solutions

Abstract

The three‐dimensional power Korteweg‐de Vries equation , 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.