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International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 183-187
http://dx.doi.org/10.1155/S0161171298000246

Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution

Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USA

Received 8 March 1996

Copyright © 1998 Hindawi Publishing Corporation. 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.

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.