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
收藏
页码：175 / 224
页数：50
相关论文
共 50 条
  • [1] Nonlinear Schrodinger equation with a random potential
    Bourgain, Jean
    [J]. ILLINOIS JOURNAL OF MATHEMATICS, 2006, 50 (01) : 183 - 188
  • [2] Perturbation theory for the nonlinear Schrodinger equation with a random potential
    Fishman, Shmuel
    Krivolapov, Yevgeny
    Soffer, Avy
    [J]. NONLINEARITY, 2009, 22 (12) : 2861 - 2887
  • [3] The nonlinear Schrodinger equation with a random potential: results and puzzles
    Fishman, Shmuel
    Krivolapov, Yevgeny
    Soffer, Avy
    [J]. NONLINEARITY, 2012, 25 (04)
  • [4] On the problem of dynamical localization in the nonlinear Schrodinger equation with a random potential
    Fishman, Shmuel
    Krivolapov, Yevgeny
    Soffer, Avy
    [J]. JOURNAL OF STATISTICAL PHYSICS, 2008, 131 (05) : 843 - 865
  • [5] The nonlinear Schrodinger equation with a potential
    Germain, Pierre
    Pusateri, Fabio
    Rousset, Frederic
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35 (06): : 1477 - 1530
  • [6] Double-humped states in the nonlinear Schrodinger equation with a random potential
    Veksler, H.
    Krivolapov, Y.
    Fishman, S.
    [J]. PHYSICAL REVIEW E, 2010, 81 (01):
  • [7] Approximation of the DNLS equation by the cubic nonlinear Schrodinger equation
    Oliveira, F
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2004, 134 : 595 - 607
  • [8] ON THE FLUID APPROXIMATION TO A NONLINEAR SCHRODINGER-EQUATION
    ERCOLANI, N
    MONTGOMERY, R
    [J]. PHYSICS LETTERS A, 1993, 180 (06) : 402 - 408
  • [9] Random input problem for the nonlinear Schrodinger equation
    Derevyanko, Stanislav A.
    Prilepsky, Jaroslaw E.
    [J]. PHYSICAL REVIEW E, 2008, 78 (04):
  • [10] The Boltzmann equation as limit of a Schrodinger equation with random potential
    Brassart, M
    [J]. ASYMPTOTIC ANALYSIS, 2004, 37 (3-4) : 189 - 214
12345