Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution (Q1380976)

Summary: The generalized nearly concentric Korteweg-de Vries equation \[ \bigl[u_\eta +u/(2\eta) +u^nu_\xi +u_{\xi\xi\xi} \bigr]_\xi+ u_{\theta \theta}/ \eta ^2=0 \] is considered. The author converts the equation into the power Kadomtsev-Petviashvili equation \[ [u_t+ u^nu_x+ u_{xxx}]_x +u_{yy} =0. \] 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.