International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 183-187
doi: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 Yunkai Chen. 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.