Critical nonlinear Schrodinger equations with and without harmonic potential

被引：76

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

[11] DETERMINATION OF BLOW-UP SOLUTIONS WITH MINIMAL MASS FOR NONLINEAR SCHRODINGER-EQUATIONS WITH CRITICAL POWER [J].

MERLE, F .

DUKE MATHEMATICAL JOURNAL, 1993, 69 (02) :427-454

[12] ON UNIQUENESS AND CONTINUATION PROPERTIES AFTER BLOW-UP TIME OF SELF-SIMILAR SOLUTIONS OF NONLINEAR SCHRODINGER-EQUATION WITH CRITICAL EXPONENT AND CRITICAL MASS [J].

MERLE, F .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (02) :203-254

[13] CONSTRUCTION OF SOLUTIONS WITH EXACTLY K-BLOW-UP POINTS FOR THE SCHRODINGER-EQUATION WITH CRITICAL NONLINEARITY [J].

MERLE, F .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 129 (02) :223-240

[14]

Merle F., 1998, P INT C MATHEMATICIA, VIII, P57

[15]

NIEDERER U, 1974, HELV PHYS ACTA, V47, P167

[16] CAUCHY-PROBLEM AND EHRENFEST LAW OF NONLINEAR SCHRODINGER-EQUATIONS WITH POTENTIALS [J].

OH, YG .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 81 (02) :255-274

[17] Similarity solutions and collapse in the attractive Gross-Pitaevskii equation [J].

Rybin, AV ;

Varzugin, GG ;

Lindberg, M ;

Timonen, J ;

Bullough, RK .

PHYSICAL REVIEW E, 2000, 62 (05) :6224-6228

[18] EXISTENCE OF SOLITARY WAVES IN HIGHER DIMENSIONS [J].

STRAUSS, WA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 55 (02) :149-162

[19] NON-LINEAR SCHRODINGER-EQUATIONS AND SHARP INTERPOLATION ESTIMATES [J].

WEINSTEIN, MI .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 87 (04) :567-576

[20] Stability of attractive Bose-Einstein condensates [J].

Zhang, J .

JOURNAL OF STATISTICAL PHYSICS, 2000, 101 (3-4) :731-746

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