Direct and inverse scattering for selfadjoint Hamiltonian systems on the line
type: Item
instance of: scholarly article
title: Direct and inverse scattering for selfadjoint Hamiltonian systems on the line
zbMATH Open document ID: 0970.34072
DOI: 10.1007/BF01200121
author: Tuncay Aktosun
author: Martin Klaus
author: C. van der Mee
published in: Integral Equations and Operator Theory
publication date: 2001-10-13T00:00:00Z
review text: An inverse scattering theory is constructed for the selfadjoint system of differential equations \[ -iJ_{2n}Y'(x,\lambda)-V(x)Y(x,\lambda)=\lambda Y(x,\lambda),\quad -\infty<x<\infty, \] on the line, with \[ J_{2n}=\left[\begin{matrix} I_n & 0 \\ 0 & -I_n\end{matrix}\right],\qquad V(x)=\left[\begin{matrix} 0 & k(x) \\ k^*(x) & 0 \end{matrix}\right], \] \(I_n\) is the identity matrix of odd order \(n\), \(k(x)\in L(-\infty,\infty)\) is the \(n\times n\)-matrix function, and \(*\) denotes the matrix conjugate transpose.
Mathematics Subject Classification ID: 34L25
Mathematics Subject Classification ID: 81U40
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 1542407
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: inverse scattering
zbMATH Keywords: Marchenko integral equation
reviewed by: V. A. Yurko
MaRDI profile type: Publication
cites work: Q5528087
cites work: Q3995225
cites work: Inverse spectral problem for differential operators with rational scattering matrix functions
cites work: Q4358792
cites work: Q5284133
cites work: Q4718324
cites work: DARLINGTON REALIZATION OF MATRIX-VALUED FUNCTIONS
cites work: Scattering and inverse scattering for first-order systems: II
cites work: Q3994426
cites work: Minimal factorization of matrix and operator functions
cites work: Wiener-Hopf factorization, inverse Fourier transforms and exponentially dichotomous operators
cites work: Q4321430
cites work: Q4040771
cites work: Factorization of matrix functions and singular integral operators
cites work: Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation
cites work: Q5594547
cites work: Classes of linear operators. Vol. I
cites work: Canonical Systems with Rational Spectral Densities: Explicit Formulas and Applications
cites work: Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications
cites work: Q4952495
cites work: Inverse scattering for the Dirac operator on the real line
cites work: Q4850020
cites work: Q4072122
cites work: Q4139037
cites work: Q3473405
cites work: Minimal factorization of selfadjoint rational matrix functions
cites work: Q4191141
cites work: Nonlinear Schrödinger equation on a semi-axis and an inverse problem associated with it
cites work: Factorization problems and operator identities
cites work: Q4289750
cites work: Spectral problems for canonical systems of equations on the axis
cites work: Q3897313
description: scientific article; zbMATH DE number 1542407