BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sandra Carillo DTSTART:20240311T080000Z DTEND:20240311T084500Z DTSTAMP:20260423T011111Z UID:NIS2024/12 DESCRIPTION:Title: Bäcklund transformations and non-Abelian nonlinear evolution equations\nby Sandra Carillo as part of Seminar-Type Workshop on Noncommutative I ntegrable Systems\n\n\nAbstract\nBäcklund transformations are well known to represent a powerful tool in investigating nonlinear differential equat ions. In particular\, we are concerned about so-called soliton equations s ince they admit soliton type solutions. The aim of the present study is tw ofold since\, on one side\, we consider the connections which can be estab lished and the induced structural properties\; on the other side\, we cons ider Bäcklund transformations as a tool to construct solutions\, admitted by nonlinear evolution equations. Hence\, first of all\, we consider the links which can be established among different nonlinear evolution equatio ns via Bäcklund transformations. Accordingly\, a net of connections among different nonlinear evolution equations is depicted in a Bäcklund Chart\ , as we term such a net of links. The attention is focussed on third order \, nonlinear evolution questions in particular\, the comparison between t he commutative (Abelian) and the non-commutative cases is analyzed. Notabl y\, a richer structure can be observed when the commutativity condition is removed. Then\, via Bäcklund transformations\, solutions of matrix modif ied KdV equation can be constructed. Finally\, some new results as well a s some problems\, currently under investigation\, concerning fifth order n onlinear evolution equations are mentioned. \nMost of the presented result s are part of a joint research project with Cornelia Schiebold\, Sundsvall University\, Sweden which involves also\, in alphabetical order\, M. Lo Schiavo\, Rome\, E. Porten\, Sundsvall\, and F. Zullo\, Brescia.\n LOCATION:https://researchseminars.org/talk/NIS2024/12/ END:VEVENT END:VCALENDAR