UBC Math Department Colloquium: Kenji Nakanishi

The Zakharov system is a coupled system of the Schrodinger equation and the acoustic wave equation to describe the Langmuir turbulence in plasma. The goal in this talk is to classify the solutions depending on the initial data, in particular to distinguish dispersive waves, solitons and blow-up, among all solutions with energy below or
slightly above the ground states. In the subsonic limit, the system is reduced to the nonlinear Schrodinger equation, but the analysis of the system is much more challenging than the latter, due to the derivative loss, the low degree of nonlinear interactions, and the loss of symmetry for scaling and momentum.
I will review the recent progress together with the ideas to resolve those obstructions.