STABLE SOLITARY WAVES WITH PRESCRIBED L2-MASS FOR THE CUBIC SCHRODINGER SYSTEM WITH TRAPPING POTENTIALS

被引：51

作者：

Noris, Benedetta ^{[1
]}

Tavares, Hugo ^{[2
]}

Verzini, Gianmaria ^{[3
]}

机构：

[1] Univ Versailles St Quentin, Lab Math Versailles, F-78035 Versailles, France

[2] Univ Lisbon, Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Dept Math, P-1049001 Lisbon, Portugal

[3] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 12期

关键词：

Cooperative and competitive elliptic systems; Gross-Pitaevskii systems; constrained critical points; Ambrosetti-Prodi type problem; orbital stability; ORBITAL STABILITY; POSITIVE SOLUTIONS; STANDING WAVES; BOUND-STATES; EXISTENCE; EQUATIONS;

D O I：

10.3934/dcds.2015.35.6085

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the cubic Schrodinger system with trapping potentials in R-N, N <= 3, or in bounded domains, we investigate the existence and the orbital stability of standing waves having components with prescribed L-2-mass. We provide a variational characterization of such solutions, which gives information on the stability through a condition of Grillakis-Shatah-Strauss type. As an application, we show existence of conditionally orbitally stable solitary waves when: a) the masses are small, for almost every scattering lengths, and b) in the defocusing, weakly interacting case, for any masses.

引用

页码：6085 / 6112

页数：28

共 36 条

[1] Thomas-Fermi Approximation for Coexisting Two Component Bose-Einstein Condensates and Nonexistence of Vortices for Small Rotation [J].

Aftalion, Amandine ;

Noris, Benedetta ;

Sourdis, Christos .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 336 (02) :509-579

[2] On the structure of fractional degree vortices in a spinor Ginzburg-Landau model [J].

Alama, Stan ;

Bronsard, Lia ;

Mironescu, Petru .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (04) :1118-1136

[3]

AMBROSETTI A., 1993, PRIMER NONLINEAR ANA, V34

[4]

Ambrosetti A., 1972, Ann. Mat. Pura Appl, V93, P231, DOI [10.1007/BF02412022, DOI 10.1007/BF02412022]

[5] Standing waves of some coupled nonlinear Schrodinger equations [J].

Ambrosetti, Antonio ;

Colorado, Eduardo .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2007, 75 :67-82

[6]

[Anonymous], 2003, COURANT LECT NOTES M

[7] Bound states for a coupled Schrodinger system [J].

Bartsch, Thomas ;

Wang, Zhi-Qiang ;

Wei, Juncheng .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2007, 2 (02) :353-367

[8] A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system [J].

Bartsch, Thomas ;

Dancer, E. Norman ;

Wang, Zhi-Qiang .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) :345-361

[9] SEMILINEAR EQUATIONS IN RN WITHOUT CONDITION AT INFINITY [J].

BREZIS, H .

APPLIED MATHEMATICS AND OPTIMIZATION, 1984, 12 (03) :271-282

[10] Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates [J].

Chang, SM ;

Lin, CS ;

Lin, TC ;

Lin, WW .

PHYSICA D-NONLINEAR PHENOMENA, 2004, 196 (3-4) :341-361

← 1 2 3 4 →