[AN] Joris van Winden: Stability and motion of solitary waves in a stochastic PFNLS equation

21 mei 2024 16:00 t/m 17:00 - Locatie: EEMCS Lecture Hall Chip | Zet in mijn agenda

The focusing nonlinear Schrödinger equation has a special solution in the form of a nonlinear solitary wave. We consider stability of this wave under small stochastic perturbations. We show that in the presence of a certain parametric forcing, the solitary wave exhibits orbital stability, meaning that the solution remains close to a suitably translated version of the wave. The parametric forcing models amplification and damping of a wave packet propagating in an optical fiber. We show stability on a timescale which is exponential in the inverse square of the noise amplitude. Using an asymptotic expansion, we also give explicit expressions for the motion of the wave, which are valid on short timescales.