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Texas A&M University
Mathematics

Events for 08/21/2020 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

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Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Alexander Tovbis, University of Central Florida

Title: Soliton and breather gases for the focusing Nonlinear Schrödinger equation (fNLS): spectral theory and possible applications

Abstract: 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". Known laws of pairwise elastic collisions allow one to write the heuristic "equation of state" for the gas of such particles.

In this talk we consider soliton and breather gases for the 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. We also discuss the recent progress and perspectives of future work, as well as some possible applications.