On one class of systems of Lax-type equations
type: Item
instance of: scholarly article
title: On one class of systems of Lax-type equations
zbMATH Open document ID: 1312.34036
author: E. V. Oliynyk
author: Anton Lunyov
published in: Journal of Mathematical Sciences (New York)
publication date: 2014-10-14T00:00:00Z
review text: The authors consider the Lax-type system \[ \begin{cases} [a(x),\gamma(x)]=0, & x\in[0,l], \\ \gamma'(x)=i[a(x),\sigma_2], & x\in[0,l], \\ \gamma(0)=\gamma^+, \\ \end{cases} \eqno(1) \] where \(a(x),\) \(\gamma(x),\) \(\sigma_2,\) and \(\gamma^+\) are self-adjoint \(n\times n\) matrices, and \([A,B]=AB-BA\) is a commutator of the matrices \(A,B\in \mathbb{C}^{n\times n}.\) All solutions of (1) are given for some cases, in particular, for the cases of a linear and a quadratic dependence of \(a(x)\) on \(\gamma(x)\).
reviewed by: Sergei A. Mazanik
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 6355169
zbMATH Keywords: triangular models
zbMATH Keywords: nonlinear differential equations
zbMATH Keywords: elliptic functions
zbMATH Keywords: self-adjoint matrices
MaRDI profile type: Publication
full work available at URL: s10958-014-1800-8
OpenAlex ID: W2054493677
cites work: Perturbation theory for linear operators.
cites work: Q3695595
cites work: Q5641692
cites work: Q5186215
DOI: 10.1007/S10958-014-1800-8
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description: scientific article; zbMATH DE number 6355169