Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution
type: Item
instance of: scholarly article
title: Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution
zbMATH Open document ID: 0895.35090
DOI: 10.1155/S0161171298000246
author: Yunkai Chen
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-09-20T00:00:00Z
full work available at URL: https://eudml.org/doc/47951
review text: 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.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 1127758
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: Kadomtsev-Petviashvili equation
zbMATH Keywords: solitary wave solution
zbMATH Keywords: cnoidal wave solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1127758