Three-dimensional Korteweg-de Vries equation and traveling wave solutions - Kenneth L. Jones (International Journal of Mathematics and Mathematical Sciences)
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.