Abstract
We prove a representation formula for solutions of Schrödinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L 2 or in the energy space of model equations arising in Bose-Einstein condensation, Abdullaev et al (2001 Nonlinearity and Disorder: Theory and Applications (NATO Science Series vol 45) ed F Abdullaev et al (Dodrecht: Kluwer)), or in fiber optics, Abdullaev et al (2000 Physica D 135 369-86). Our results also give a justification of diffusion-approximation for stochastic nonlinear Schrödinger equations.
| Original language | English |
|---|---|
| Pages (from-to) | 2993-3022 |
| Number of pages | 30 |
| Journal | Nonlinearity |
| Volume | 25 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2012 Nov |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics
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Bouard, A. D., & Fukuizumi, R. (2012). Representation formula for stochastic Schrödinger evolution equations and applications. Nonlinearity, 25(11), 2993-3022. https://doi.org/10.1088/0951-7715/25/11/2993