Speaker:

Eric Gautier

Title:

Two Applications of Large Deviations to Random Perturbations of Nonlinear Dispersive Waves

Abstract:

We present applications of sample path large deviations for two stochastic nonlinear dispersive wave equations.
The first models are motivated by optics and are described by stochastic nonlinear Schrodinger equations. In long-haul soliton based communication systems amplification devices are used to counterbalance for loss in the fiber line. Different types of noises of additive or multiplicative types are considered in physics and depend on the type of amplification. Two processes are mainly responsible for error in soliton transmission. They are the fluctuation of the energy and arrival time of the pulse. Qualitative behavior in the parameters of these processes in the small noise asymptotic are obtained without relying on collective coordinate approximation.
The second application is related to the stochastic Korteweg-de Vries equation.
Typical exit times from a neighborhood of the soliton and randomly modulated soliton are compared and their order in the amplitude of the noise characterized.
These are joint works with respectively Arnaud Debussche and Anne de Bouard.

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