Symmetries and soliton solutions of nonlinear equations
type: Item
instance of: scholarly article
title: Symmetries and soliton solutions of nonlinear equations
zbMATH Open document ID: 0584.35006
DOI: 10.1007/BF01017835
author: A. N. Leznov
author: V. I. Man'ko
author: Sergey M. Chumakov
published in: Theoretical and Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: One of the popular ways to construct a family of soliton-type solutions of a system of partial differential equations is to derive both the family and the system from the same source. This is exactly what is done in the paper. Let g be a 2-parameter family of finite-dimensional representations of a Lie group (x,y-parameters), and \[ (\partial g/\partial x)| g=U(x,y);\quad (\partial g/\partial y)| g=V(x,y). \] Then from Cartan-Maurer equation \[ \partial U/\partial y-\partial V/\partial x- [U,V]=0 \] one derives a system of p.d.e. Explicit formulae are given for soliton solutions of the system, which originate from the same Cartan- Maurer equation.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 22E70
zbMATH DE Number: 3935550
zbMATH Keywords: soliton-type solutions
zbMATH Keywords: Lie group
zbMATH Keywords: Cartan-Maurer equation
MaRDI profile type: Publication
cites work: Method for Solving the Korteweg-deVries Equation
cites work: Q3732103
cites work: Ordinary second-order differential equations and soliton solutions connected with the algebra sl(2,\({\mathbb{C}})\)
cites work: A new class of Lie algebras
full work available at URL: https://doi.org/10.1007/bf01017835
OpenAlex ID: W2072207268
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description: scientific article; zbMATH DE number 3935550