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Soliton and breather gases for integrable equations

Alexander Tovbis
University of Central Florida
Wednesday, March 3, 2021 - 16:00 to 17:00
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. 


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