| Abstract: |
| In this talk, I will present some results on the Cauchy problem and the simulation of a randomly modulated nonlinear Schrodinger equation. This equation models the propagation of light pulses in fiber optics with a random dispersion management. In an asymptotic regime, this random modulation gives rise to the white noise dispersion which has a strong stabilizing effect and improves the well-posedness of the equation. In particular, new Strichartz estimates will be discussed. Moreover, in order to account for the small scale fluctuations of the noise, one has to rely on asymptotic preserving schemes to obtain accurate simulations. We will discuss a Lie splitting scheme which well suited for this task. |
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