On a dynamic system arising from a finite-dimensional approximation of the Schrödinger equation
type: Item
instance of: scholarly article
title: On a dynamic system arising from a finite-dimensional approximation of the Schrödinger equation
zbMATH Open document ID: 0840.34090
DOI: 10.1007/BF02362413
published in: Mathematical Notes
publication date: 1996-07-09T00:00:00Z
review text: The system of ordinary differential equations (1) \(J\dot z= \nabla_z H(z, \sigma)\), \(\dot\sigma J= [\sigma J, JH''_0]\) is studied. The author shows that system (1) is Hamiltonian with respect to a Poisson bracket that is the direct sum of the usual Poisson bracket on \(\mathbb{R}^{2n}\) and the linear Poisson bracket on the Lie algebra \(\text{sp}(2n, \mathbb{R})\), to which the matrix \(\sigma J\) belongs. The system (1) is studied in the case corresponding to a one-dimensional anharmonic oscillator. The normal form method is used to investigate the behavior of solutions; in particular, the family of periodic solutions is described.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 830729
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: finite-dimensional approximation
zbMATH Keywords: Lie algebra
zbMATH Keywords: Hamiltonian
zbMATH Keywords: one-dimensional anharmonic oscillatory
zbMATH Keywords: normal form method
zbMATH Keywords: periodic solutions
author: Sergey Yu. Sadov
reviewed by: Laura Iulia Aniţa
MaRDI profile type: Publication
cites work: Q4275429
cites work: Q3961135
cites work: Q3138307
full work available at URL: https://doi.org/10.1007/bf02362413
OpenAlex ID: W2099387786
description: scientific article; zbMATH DE number 830729