Aikaterini Gkogkou (Tulane University) – The formation of a soliton gas condensate for the focusing Nonlinear Schrödinger equation

In this talk, we consider the focusing Nonlinear Schrödinger (NLS) equation and its multisoliton solution when the number of solitons grows to infinity. We discover configurations of multi-soliton solutions that exhibit the formation of a soliton gas condensate. Specifically, we show that, when the associated discrete eigenvalues accumulate on two bounded horizontal segments in the complex plane and the associated norming constants are bounded away from zero, the solution to the focusing NLS equation is described by a rapidly oscillatory elliptic wave with constant velocity, on compact subsets of the $(x,t)$ domain.