Two topics of the integrable soliton equation
type: Item
instance of: scholarly article
title: Two topics of the integrable soliton equation
zbMATH Open document ID: 0850.35087
DOI: 10.1007/BF01017057
published in: Theoretical and Mathematical Physics
publication date: 1996-09-03T00:00:00Z
review text: I summarize some results obtained recently. The first topic is the breaking soliton equations in \(2+ 1\)-dimensional case. Some typical equations are deduced from the nonisospectral zero curvature equation. The Darboux transformations can be used to find the breaking soliton solutions of these equations, the algebraic properties of them are also considered. The second topic is the separation of variables for the soliton equations by constraints via Lax pair. The motivation of this topic is in the discovery of the similarity of the Fourier analysis and superposition rule for linear equations and the nonlinear Fourier analysis and nonlinear superposition for soliton equations.
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 907329
zbMATH Keywords: breaking soliton equations
zbMATH Keywords: Darboux transformations
zbMATH Keywords: separation of variables
zbMATH Keywords: Lax pair
zbMATH Keywords: nonlinear Fourier analysis
zbMATH Keywords: nonlinear superposition for soliton equations
author: Yi-Shen Li
MaRDI profile type: Publication
cites work: Constraints of the Kadomtsev–Petviashvili hierarchy
cites work: Wave solutions of a (2+1)-dimensional generalization of the nonlinear Schr dinger equation
cites work: Soliton solutions in an integrable chiral model in 2+1 dimensions
cites work: Integrable and solvable systems, and relations among them
full work available at URL: https://doi.org/10.1007/bf01017057
OpenAlex ID: W185465656
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description: scientific article; zbMATH DE number 907329