Paper Info
Title
The Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential
Abstract
The nonlinear Schrodinger equation with general nonlinearity of polynomial growth and harmonic con. ning potential is considered. More precisely, the con. ning potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground state of the dominating harmonic oscillator is shown to be propagated, and the lower-dimensional modulation wave function again satisfies a nonlinear Schrodinger equation. The main tools of the analysis are energy and Strichartz estimates, as well as two anisotropic Sobolev inequalities. As an application, the dimension reduction of the three-dimensional Gross - Pitaevskii equation is discussed, which models the dynamics of Bose - Einstein condensates.
Year
DOI
Venue
2005
10.1137/040614554
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
energy estimates,Strichartz estimates,anisotropic Sobolev embedding,Gross-Pitaevskii equation,Bose-Einstein condensate
Gross–Pitaevskii equation,Ground state,Nonlinear system,Mathematical analysis,Schrödinger equation,Harmonic,Wave function,Nonlinear Schrödinger equation,Harmonic oscillator,Mathematics
Journal
Volume
Issue
ISSN
37
1
0036-1410
Citations 
PageRank 
References 
2
1.39
1
Authors
4
Name
Order
Citations
PageRank
Naoufel Ben Abdallah1398.18
Florian Méhats28014.01
Christian Schmeiser3103.90
Rada M. Weishäupl421.39