UPPER SEMICONTINUITY OF ATTRACTORS FOR THE KLEIN–GORDON–SCHRÖDINGER EQUATION

In this paper, we consider the Klein–Gordon–Schröodinger equation defined on Rn (n ≤ 3) and Ωm = {x ∈ Rn : |x| ≤ m}. Let [Formula: see text] and [Formula: see text] be the global attractors of the equation corresponding to Rn and Ωm, respectively. Then we prove that for any neighborhood U of [Formula: see text], the global attractor [Formula: see text] enters U when m is large enough.

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Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for k-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-Schrödinger Equation

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-006-0323-6 ◽

2006 ◽

Vol 22 (3) ◽

pp. 469-486

Author(s):

Fu-qi Yin ◽

Sheng-fan Zhou

Keyword(s):

Dynamical System ◽

Schrödinger Equation ◽

Global Attractor ◽

Schrodinger Equation ◽

Upper Semicontinuity ◽

Dimensional Lattice ◽

Lattice Dynamical System ◽

Klein Gordon

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Global Attractors for the Klein–Gordon–Schrödinger Equation in Unbounded Domains

Journal of Differential Equations ◽

10.1006/jdeq.2000.3827 ◽

2001 ◽

Vol 170 (2) ◽

pp. 281-316 ◽

Cited By ~ 42

Author(s):

Kening Lu ◽

Bixiang Wang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Unbounded Domains ◽

Global Attractors ◽

Klein Gordon

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Regularity of the global attractor for the Klein-Gordon-Schrödinger equation

Mathematical Methods in the Applied Sciences ◽

10.1002/(sici)1099-1476(19991125)22:17<1535::aid-mma92>3.0.co;2-5 ◽

1999 ◽

Vol 22 (17) ◽

pp. 1535-1554 ◽

Cited By ~ 4

Author(s):

Horst Lange ◽

Bixiang Wang

Keyword(s):

Schrödinger Equation ◽

Global Attractor ◽

Schrodinger Equation ◽

Klein Gordon

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Analysis of a Fourier pseudo-spectral conservative scheme for the Klein–Gordon–Schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2017.1366460 ◽

2017 ◽

Vol 95 (1) ◽

pp. 36-60 ◽

Cited By ~ 3

Author(s):

Jialing Wang ◽

Yushun Wang ◽

Dong Liang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Conservative Scheme ◽

Klein Gordon ◽

Pseudo Spectral

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Energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.07.003 ◽

2021 ◽

Author(s):

Longbin Wu ◽

Qiang Ma ◽

Xiaohua Ding

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Klein Gordon

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Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.02.096 ◽

2011 ◽

Vol 217 (19) ◽

pp. 7818-7830 ◽

Cited By ~ 2

Author(s):

Emna Ezzoug ◽

Wided Kechiche ◽

Ezzeddine Zahrouni

Keyword(s):

Schrödinger Equation ◽

Point Defect ◽

Global Attractor ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

Nonlinear Schrödinger ◽

Finite Dimensional

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Analysis of a conservative high-order compact finite difference scheme for the Klein–Gordon–Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.02.018 ◽

2019 ◽

Vol 358 ◽

pp. 84-96 ◽

Cited By ~ 2

Author(s):

Jialing Wang ◽

Dong Liang ◽

Yushun Wang

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Schrodinger Equation ◽

High Order ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference ◽

Klein Gordon

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Development of the Schrödinger equation and Klein-Gordon equation via Bellman's principle of optimality

Physics Letters A ◽

10.1016/0375-9601(87)90624-4 ◽

1987 ◽

Vol 124 (4-5) ◽

pp. 220-222 ◽

Cited By ~ 1

Author(s):

C.P. Kwong

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Gordon Equation ◽

Principle Of Optimality ◽

Klein Gordon ◽

Bellman's Principle ◽

Bellman’S Principle ◽

Klein Gordon Equation

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Covariant Variational Evolution and Jacobi brackets: Fields

Modern Physics Letters A ◽

10.1142/s0217732320502065 ◽

2020 ◽

Vol 35 (23) ◽

pp. 2050206

Author(s):

F. M. Ciaglia ◽

F. Di Cosmo ◽

A. Ibort ◽

G. Marmo ◽

L. Schiavone

Keyword(s):

Schrödinger Equation ◽

Variational Problem ◽

Schrodinger Equation ◽

Contact Geometry ◽

Klein Gordon ◽

Variational Evolution

The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter[Formula: see text] is extended to the case of the multisymplectic formulation of the free Klein–Gordon theory and of the free Schrödinger equation.

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