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The finite dimension behavior of the Schrödinger equation with nonlocal integral nonlinearity

The finite dimension behavior of the Schrödinger equation with nonlocal integral nonlinearity In this paper we discuss the long time behavior of the initial problem $$iu_t + u_{xx} + \beta \left| u \right|^p u + \gamma u\int_{ - \infty }^x {\left| u \right|^2 dx + iku = g,} $$ $$u\left| {_{t = 0} } \right. = u^0 .$$ We show that in a weighted Hilbert space there, exists a global attractor which is weakly compact and has finite Hausdorff and fractal dimension. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The finite dimension behavior of the Schrödinger equation with nonlocal integral nonlinearity

Haiyang, Huang
Acta Mathematicae Applicatae Sinica , Volume 15 (1) – Jul 4, 2007
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02677394
Publisher site
See Article on Publisher Site

Abstract

In this paper we discuss the long time behavior of the initial problem $$iu_t + u_{xx} + \beta \left| u \right|^p u + \gamma u\int_{ - \infty }^x {\left| u \right|^2 dx + iku = g,} $$ $$u\left| {_{t = 0} } \right. = u^0 .$$ We show that in a weighted Hilbert space there, exists a global attractor which is weakly compact and has finite Hausdorff and fractal dimension.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 4, 2007

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