Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect
type: Item
instance of: scholarly article
title: Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect
zbMATH Open document ID: 1229.65169
author: Emna Ezzoug
author: Wided Kechiche
author: Ezzeddine Zahrouni
published in: Applied Mathematics and Computation
publication date: 2011-06-14T00:00:00Z
review text: The authors consider a generalization of a cubic nonlinear Schrödinger equation in one space dimension with a point defect, obtained by adding a linear term to the differential operator and the right hand side, containing a delta-function. The problem is discretized in time by the Crank-Nicolson scheme. Different properties of the solution are investigated and in particular the well-possedness of the scheme is established. It is proved that the obtained semi-discrete problem can be considered as a discrete infinite dynamical system with a global attractor. The conditions of compactness and finite dimensionality of this global attractor are established.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 5907629
zbMATH Keywords: semi-discrete scheme
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: splitting method
zbMATH Keywords: global attractor
zbMATH Keywords: discrete infinite dynamical system
reviewed by: Snezhana Gocheva-Ilieva
MaRDI profile type: Publication
full work available at URL: j.amc.2011.02.096
OpenAlex ID: W1998588914
cites work: Discrete Schrödinger equations and dissipative dynamical systems
cites work: Regularity of the attractor for a weakly damped nonlinear Schrödinger equation on \(\mathbb{R}\)
cites work: On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
cites work: Global attractors for damped semilinear wave equations.
cites work: A Relaxation Scheme for the Nonlinear Schrödinger Equation
cites work: Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
cites work: Q5522517
cites work: Attractors for second-order evolution equations with a nonlinear damping
cites work: Finite-difference solutions of a non-linear Schrödinger equation
cites work: Semi-discrete weakly damped nonlinear 2-D Schrödinger equation.
cites work: Nonlinear Schrödinger equation with a point defect
cites work: Strong NLS soliton-defect interactions
cites work: Regularity of the attractor for a weakly damped nonlinear schrödinger equation
cites work: On a time discretization of a weakly damped forced nonlinear Schrödinger equation
cites work: Q4039920
cites work: Long-time behaviour for weakly damped driven nonlinear Schrödinger equations in \(\mathbb{R}^ N, N\leq 3\)
cites work: Q3645637
cites work: Q4550349
cites work: Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
cites work: Q3808524
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
cites work: Attractors and dimensions for discretizations of a weakly damped Schrödinger equation and a Sine-Gorden equation
DOI: 10.1016/J.AMC.2011.02.096
description: scientific article; zbMATH DE number 5907629