Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications
type: Item
instance of: scholarly article
title: Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications
zbMATH Open document ID: 0917.34074
author: I. Gohberg
author: Marinus Kaashoek
author: Alexander L. Sakhnovich
published in: Journal of Differential Equations
publication date: 1999-08-05T00:00:00Z
review text: Differential systems called pseudo-canonical are considered on the half-axis \(x\geq 0\): \[ {d\over dx}u(x,\lambda) =i\bigl(\lambda j+V(x) \bigr) u(x, \lambda), \] with \[ j=\left[ \begin{matrix} I_m & 0\\ 0 & -I_m\end{matrix} \right], \quad V=\left[ \begin{matrix} 0 & v\\ v^* & 0\end{matrix} \right], \] \(u\) and \(U\) are \(2m\times 2m\) matrix functions, \(v\) is an \(m\times m\) locally summable matrix of a special form. The corresponding operator has both selfadjoint and skew selfadjoint parts. The basic role belongs to the introduced Weyl function. Solutions to the direct and inverse spectral problems are derived. State space methods from mathematical system theory are used. Applications to the corresponding matrix nonlinear Schrödinger equation and to the modified Korteweg-de Vries equation are given.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 34B20
zbMATH DE Number: 1212366
zbMATH Keywords: fundamental solution
zbMATH Keywords: Weyl function
zbMATH Keywords: pseudo-exponential potentials
zbMATH Keywords: matrix modified
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: nonlinear Schrödinger equation
MaRDI profile type: Publication
OpenAlex ID: W1963741627
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DOI: 10.1006/JDEQ.1998.3428
description: scientific article; zbMATH DE number 1212366