BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Tovbis (University of Central Florida) DTSTART:20200821T185000Z DTEND:20200821T195000Z DTSTAMP:20260423T004140Z UID:MPHA/11 DESCRIPTION:Title: So liton and breather gases for the focusing Nonlinear Schrödinger equation (fNLS): spectral theory and possible applications\nby Alexander Tovbis (University of Central Florida) as part of TAMU: Mathematical Physics and Harmonic Analysis Seminar\n\n\nAbstract\nIn the talk we introduce the ide a of an "integrable gas" as a collection of large random ensembles of spec ial localized solutions (solitons\, breathers) of a given integrable syste m. These special solutions can be treated as "particles". Known laws of pa irwise elastic collisions allow one to write the heuristic "equation of st ate" for the gas of such particles.\n\nIn this talk we consider soliton an d breather gases for the fNLS as special thermodynamic limits of finite ga p (nonlinear multi phase wave) fNLS solutions. In this limit the rate of g rowth of the number of bands is linked with the rate of (simultaneous) shr inkage of the size of individual bands. This approach leads to the derivat ion of the equation of state for the gas and its certain limiting regimes (condensate\, ideal gas limits)\, as well as construction of various inter esting examples. We also discuss the recent progress and perspectives of f uture work\, as well as some possible applications.\n LOCATION:https://researchseminars.org/talk/MPHA/11/ END:VEVENT END:VCALENDAR