BZ Seminar in Analysis: Herbert Koch (Universität Bonn)

Phase space and solitons for the Gross-Pitaevskii equation

The Gross-Pitaevskii equation is the defocusing nonlinear Schrödinger equation with amplitude 1 at infinity. The set of functions with finite energy is a nonlinear set of functions, modulo the multiplication by complex units. We define a set of metrics on this space such that the evolution is continuous and the trivial solution is stable. This metric space is topologically a sphere, with the consequence that many natural functionals are multivalued. Finally I will discuss Bäcklund transforms leading to stability of sets of multisolitons in this metric. It is natural to conjecture asymptotic stability and even soliton resolution. A new feature is the use of the same metric for the initial distance and stability.

Veranstaltung übernehmen als iCal