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 |
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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