Critical nonlinear Schrodinger equations with and without harmonic potential

被引：75

作者：

Carles, R ^{[1
]}

机构：

[1] Univ Bordeaux 1, UMR 5466 CNRS, F-33405 Talence, France

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2002年 / 12卷 / 10期

关键词：

critical nonlinear Schrodinger equation; harmonic potential; Bose-Einstein condensation; blow-up in finite time; wave collapse;

D O I：

10.1142/S0218202502002215

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use a change of variables that turns the critical nonlinear Schrodinger equation into the critical nonlinear Schrodinger equation with isotropic harmonic potential, in any spare dimension. This change of variables is isometric on L-2, and bijective on some time intervals. Using the known results for the critical nonlinear Schrodinger equation, this provides information for the properties of Bose-Einstein condensate in spare dimension one and two. We discuss in particular the wave collapse phenomenon.

引用

页码：1513 / 1523

页数：11

共 20 条

[1] Bose-Einstein condensation of lithium: Observation of limited condensate number [J].

Bradley, CC ;

Sackett, CA ;

Hulet, RG .

PHYSICAL REVIEW LETTERS, 1997, 78 (06) :985-989

[2] EVIDENCE OF BOSE-EINSTEIN CONDENSATION IN AN ATOMIC GAS WITH ATTRACTIVE INTERACTIONS [J].

BRADLEY, CC ;

SACKETT, CA ;

TOLLETT, JJ ;

HULET, RG .

PHYSICAL REVIEW LETTERS, 1995, 75 (09) :1687-1690

[3]

Carles R, 2000, INDIANA U MATH J, V49, P475

[4]

CARLES R, IN PRESS ANN I H POI

[5]

CARLES R, 2001, SEM X EDP 2001 2002

[6]

CAZENAVE T, 1989, LECT NOTES MATH, V1394, P18

[7]

CAZENAVE T, 1993, TEXT MET MAT, V26

[8]

COHENTANNOUDJI C, 1998, COURS COLL FRANCE

[9] Low-dimensional Bose liquids: Beyond the Gross-Pitaevskii approximation [J].

Kolomeisky, EB ;

Newman, TJ ;

Straley, JP ;

Qi, XY .

PHYSICAL REVIEW LETTERS, 2000, 85 (06) :1146-1149

[10]

KWONG MK, 1989, ARCH RATION MECH AN, V105, P243

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