Catherine Sulem - Nonlinear Schrödinger equation and wave collapse

Wave propagation describes phenomena in many physical systems : for example water waves, laser beams, plasmas. Wave collapse or blow-up means that some physical quantities change by several orders of magnitude over relatively short times. The most basic mathematical model of wave dynamics is the Nonlinear Schrödinger Equation. The formation of singularities in a solution reflects blow-up or collapse.

Blowing-up of solutions is important because the character of the singularity strongly affects the physics, even when the blow-up is eventually arrested by effects such as dissipation or coupling. I will describe a variety of approaches to the understanding of these phenomena, ranging from mathematical analysis to formal asymptotic expansions and numerical simulations.