Two-dimensional amplitude evolution equations for nonlinear dispersive waves on thin films
type: Item
instance of: scholarly article
title: Two-dimensional amplitude evolution equations for nonlinear dispersive waves on thin films
zbMATH Open document ID: 0664.76036
DOI: 10.1016/0167-2789(89)90238-8
author: S. Melkonian
author: S. A. Maslowe
published in: Physica D
publication date: 1989-01-01T00:00:00Z
review text: This paper deals with amplitude equations for two-dimensional long waves on the free surface of a thin film flowing down an inclined plane. These equations are generalizations of the result that in the one-dimensional case the Korteweg-de Vries equation applies in a certain limit. Two distinct scalings are considered here and parallel N-soliton solutions are shown to exist in each case. In addition, one of these equations admits two-dimensional solitary waves, but we show that neither equation possesses obliquely-interacting soliton solutions.
Mathematics Subject Classification ID: 76D08
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4087241
zbMATH Keywords: two-dimensional long waves
zbMATH Keywords: free surface
zbMATH Keywords: thin film flowing
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: scalings
zbMATH Keywords: obliquely-interacting soliton solutions
MaRDI profile type: Publication
full work available at URL: 0167-2789(89)90238-8
OpenAlex ID: W2026287896
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description: scientific article; zbMATH DE number 4087241