The nonlinear Schroedinger equation: Solitons dynamics

被引：9
作者：
Benci, Vieri [2 ]
Ghimenti, Marco [1 ]
Micheletti, Anna Maria [2 ]
机构：
[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy
[2] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 12期
关键词：
Soliton dynamics; Nonlinear Schroedinger equation; Orbital stability; Concentration phenomena; Semiclassical limit; LINEAR SCHRODINGER EQUATIONS; SOLITARY WAVES; SEMICLASSICAL LIMIT; STABILITY THEORY; GROUND-STATES; EXISTENCE; DIMENSIONS; EVOLUTION; SYMMETRY;
D O I：
10.1016/j.jde.2010.09.026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h -> 0. We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter q(h)(t) satisfies the equation q(h)(t) + del V (q(h) (t)) = H-h(t) where sup(t is an element of R)vertical bar H-h(t)vertical bar -> 0 as h -> 0. (C) 2010 Elsevier Inc. All rights reserved.
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页码：3312 / 3341
页数：30
相关论文
共 26 条
  • [1] Bakry D, 1995, INDIANA U MATH J, V44, P1033
  • [2] Bellazzini J, 2007, ADV NONLINEAR STUD, V7, P439
  • [3] Bellazzini J, 2009, DYNAM PART DIFFER EQ, V6, P311
  • [4] BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
  • [5] Bronski JC, 2000, MATH RES LETT, V7, P329
  • [6] ORBITAL STABILITY OF STANDING WAVES FOR SOME NON-LINEAR SCHRODING EQUATIONS
    CAZENAVE, T
    LIONS, PL
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 85 (04) : 549 - 561
  • [7] Cazenave T, 2003, Semilinear Schrodinger Equations
  • [8] Solitary wave dynamics in an external potential
    Fröhlich, J
    Gustafson, S
    Jonsson, BLG
    Sigal, IM
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 250 (03) : 613 - 642
  • [9] Gelfand IM., 1963, Calculus of variations
  • [10] Gidas B., 1981, Math. Anal. Appl., VofAdv, P369
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