A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x,y plane
type: Item
instance of: scholarly article
title: A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x,y plane
zbMATH Open document ID: 0647.35077
DOI: 10.1007/BF01225378
author: V. K. Mel'nikov
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The author proposes a new method which is different to the inverse scattering method to find explicit expressions for a multi-soliton solution of the system of equations describing the interaction of a long wave with a short wave packet on the x, y plane. This method is based on the theory of matrices. If the system is independent of y, then the system of the coupled Boussinesq-nonlinear Schrödinger equations can be obtained, it is an interesting result.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4056201
zbMATH Keywords: explicit expressions
zbMATH Keywords: multi-soliton
zbMATH Keywords: interaction
zbMATH Keywords: long wave
zbMATH Keywords: short wave packet
zbMATH Keywords: Boussinesq-nonlinear Schrödinger equations
reviewed by: Boling Guo
MaRDI profile type: Publication
cites work: On equations for wave interactions
cites work: Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
cites work: \(N\)-soliton solution of the two-dimensional Korteweg-deVries equation
cites work: Q5621188
full work available at URL: https://doi.org/10.1007/bf01225378
OpenAlex ID: W2030251701
description: scientific article; zbMATH DE number 4056201