NONLINEAR SCHRODINGER EQUATION WITH TIME DEPENDENT POTENTIAL

被引：81

作者：

Carles, Remi ^{[1
,2
]}

机构：

[1] Univ Montpellier 2, F-34095 Montpellier, France

[2] CNRS, UMR 5149, F-34095 Montpellier, France

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2011年 / 9卷 / 04期

关键词：

Nonlinear Schrodinger equation; time dependent external potential; Avron-Herbst formula; lens transform; large time behavior; FUNDAMENTAL SOLUTION; CONVERGENCE; POINTS; STATES;

D O I：

10.4310/CMS.2011.v9.n4.a1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by physics (Bose-Einstein condensation), and appears also as a preparation for the analysis of the propagation of wave packets in a nonlinear context. The main aspect considered in this paper is the growth of high Sobolev norms of the solution when the potential is exactly quadratic in space. Such a control is needed to study the large time propagation of nonlinear coherent states.

引用

页码：937 / 964

页数：28

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