The nonlinear Schroedinger equation: Solitons dynamics

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Benci, Vieri²  Ghimenti, Marco¹  Micheletti, Anna Maria² 

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[2] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy

关键词: Soliton dynamics;    Nonlinear Schroedinger equation;    Orbital stability;    Concentration phenomena;    Semiclassical limit;   

DOI  :  10.1016/j.jde.2010.09.026

来源: Elsevier

【 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.

【 授权许可】

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