Lie symmetries and invariant solutions of the shallow-water equation
type: Item
instance of: scholarly article
title: Lie symmetries and invariant solutions of the shallow-water equation
zbMATH Open document ID: 0864.76018
DOI: 10.1016/0020-7462(95)00063-1
published in: International Journal of Non-Linear Mechanics
publication date: 1997-06-24T00:00:00Z
review text: We investigate the Lie symmetries and similarity reductions of the new completely integrable dispersive shallow water equation, through classical and non-classical methods. We compare the similarity reduction thus obtained with the similarity reduction obtained by the direct method. The resultant ordinary differential equation satisfies the Painlevé property and the ARS conjecture. We also point out how the similarity reduction of the present integrable system differs from that of the non-integrable, but closely related, Benjamin-Bono-Mahoney equation.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 966573
zbMATH Keywords: similarity reduction
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: Painlevé property
zbMATH Keywords: ARS conjecture
zbMATH Keywords: Benjamin-Bono-Mahoney equation
author: M. Senthilvelan
author: M. Lakshmanan
MaRDI profile type: Publication
full work available at URL: 0020-7462(95)00063-1
OpenAlex ID: W2068491392
description: scientific article