Math Phys Seminar: Sourav Chatterjee (Courant Inst. NYU) 'Invariant measures and the soliton resolution conjecture'
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution. Considered to be one of the fundamental problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation till date. I will present a theorem that proves a "statistical version" of this conjecture at mass-subcritical nonlinearity. The proof involves a combination of techniques from large deviations, PDE, harmonic analysis and bare hands probability theory.
Location: Jadwin A06
Date/Time: 03/27/12 at 3:30 pm - 03/27/12 at 5:00 pm
Category: Mathematical Physics Seminar