Approximation diffusion for the Nonlinear Schrodinger equation with a random potential

被引：0

作者：

Barrue, Gregoire ^{[1
]}

Debussche, Arnaud ^{[2
,3
]}

Tusseau, Maxime ^{[1
]}

机构：

[1] Univ Rennes, CNRS, IRMAR, UMR 6625, F-35000 Rennes, France

[2] Univ Rennes, F-35000 Rennes, France

[3] CNRS, IUF, IRMAR UMR 6625, F-35000 Rennes, France

来源：

ASYMPTOTIC ANALYSIS | 2024年 / 138卷 / 03期

关键词：

Nonlinear Schrodinger equation; diffusion-approximation;

D O I：

10.3233/ASY-241894

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the stochastic Nonlinear Schrodinger (NLS) equation is the limit of NLS equation with random potential with vanishing correlation length. We generalize the perturbed test function method to the context of dispersive equations. Apart from the difficulty of working in infinite dimension, we treat the case of random perturbations which are not assumed uniformly bounded.

引用

页码：175 / 224

页数：50

共 50 条

[31] NONLINEAR SCHRODINGER EQUATION WITH TIME DEPENDENT POTENTIAL
Carles, Remi
[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2011, 9 (04) : 937 - 964
[32] Diffusion approximation for the convection-diffusion equation with random drift
Komorowski, T
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2001, 121 (04) : 525 - 550
[33] Diffusion approximation for the convection-diffusion equation with random drift
Tomasz Komorowski
[J]. Probability Theory and Related Fields, 2001, 121 : 525 - 550
[34] Existence and approximation of some radial solutions of a nonlinear Schrodinger equation
Vrdoljak, B
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1996, 76 : 703 - 704
[35] Numerical approximation of singular solutions of the damped Nonlinear Schrodinger equation
Akrivis, GD
Dougalis, VA
Karakashian, OA
McKinney, WR
[J]. ENUMATH 97 - 2ND EUROPEAN CONFERENCE ON NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS, 1998, : 117 - 124
[36] Nonlinear Schrodinger Approximation for the Electron Euler-Poisson Equation
Liu, Huimin
Pu, Xueke
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2023, 44 (03) : 361 - 378
[37] A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRODINGER EQUATION
Shi, Dongyang
Liao, Xin
Wang, Lele
[J]. ACTA MATHEMATICA SCIENTIA, 2017, 37 (03) : 584 - 592
[38] CONVERGENCE TO SPDE OF THE SCHRODINGER EQUATION WITH LARGE, RANDOM POTENTIAL
Zhang, Ningyao
Bal, Guillaume
[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2014, 12 (05) : 825 - 841
[39] Statistical properties of the one dimensional Anderson model relevant for the nonlinear Schrodinger equation in a random potential
Michaely, E.
Fishman, S.
[J]. EUROPEAN PHYSICAL JOURNAL B, 2012, 85 (11):
[40] DETERMINING A RANDOM SCHRODINGER EQUATION WITH UNKNOWN SOURCE AND POTENTIAL
Li, Jingzhi
Liu, Hongyu
Ma, Shiqi
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (04) : 3465 - 3491

← 1 2 3 4 5 →