Title: Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation.
Abstract:
Solitons and breathers are localized solutions of integrable systems that can be viewed as “quasi-particles” of complex statistical objects called soliton and breather gases.
In this talk, we discuss spectral theory of a generalized breather gas by considering a special, thermodynamic type limit of multi-phase (finite-gap) solutions of the focusing nonlinear Schrödinger equation. The family of generalized breather gases includes gas of solitons and gas of breathers (solitons on finite background) as most important particular cases.
We consider several particularly interesting examples of the generalized breather gas including the so-called bound state soliton gas, multi-component breather gas, circular soliton gas etc., as well as some limiting regimes (condensate and ideal gas limits) of the gas.
Alexi Morin-Duchesne
