International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 183-187
doi:10.1155/S0161171298000246
Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution
Yunkai Chen
Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USA
Abstract
The generalized nearly concentric Korteweg-de Vries equation [un+u/(2η)+u2uζ+uζζζ]ζ+uθθ/η2=0 is considered. The author converts the equation into the power Kadomtsev-Petviashvili equation [ut+unux+uxxx]x+uyy=0. Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.