Large deviations and support results for nonlinear Schrodinger equations with additive noise and applications

Details Large deviations and support results for nonlinear Schrodinger equations with additive noise and applications Large deviations and support results for nonlinear Schrodinger equations with additive noise and applications

2004-06-18

arxiv.org/abs/math/0406362v1

ESAIM: P&S, April 2005, Vol. 9, pp. 74-97

Mathematics

Analysis of PDEs

Scientific paper

10.1051/ps:2005005

Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrodinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored space wise. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with projective limit topologies. In this setting, the support of the law of the solution is also characterized. As a consequence, results on the law of the blow-up time and asymptotics when the noise converges to zero are obtained. An application to the transmission of solitary waves in fiber optics is also given.

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