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

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.

Keywords

• Korteweg-de Vries equation
• Kadomtsev-Petviashvili equation
• solitary wave solution
• cnoidal wave solution.