In the talk we introduce the idea of an "integrable gas" as a collection of large random ensembles of special localized solutions (solitons, breathers) of a given integrable system. These special solutions can be
treated as "particles".

In this talk we consider soliton and breather gases for the focusing Nonlinear Schroedinger Equation (fNLS) as special thermodynamic limits of finite gap (nonlinear multi phase wave) fNLS solutions. In this limit the rate of growth of the number of bands is linked with the rate of (simultaneous) shrinkage of the size of individual bands. This approach leads to the derivation of the equation of state for the gas and its certain limiting regimes (condensate, ideal gas limits), as well as construction of various interesting examples. Speaker(s): Alexander Tovbis (University of Central Florida)