BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:V.E. Adler (Landau Institute for Theoretical Physics) DTSTART:20240425T110000Z DTEND:20240425T120000Z DTSTAMP:20260423T005825Z UID:mmandim/75 DESCRIPTION:Title: Negative symmetries: properties and applications. Continuation\, part 2\nby V.E. Adler (Landau Institute for Theoretical Physics) as part of Ma thematical models and integration methods\n\n\nAbstract\nOne of the defini tions of negative symmetry of an integrable equation is given by the formu la $u_t=(R-a)^{-1}(0)$ where $R$ is the recursion operator and $a$ is a pa rameter. This extension of symmetry algebra is of interest from different points of view: 1) negative symmetry can be interesting as an independent equation\; 2) it contains information about the entire integrable hierarch y\, since the expansion in parameter a serves as a generating function for higher symmetries\; 3) there are applications in the problem of construct ing finite-dimensional reductions\, especially in combination with classic al symmetries (which provides an approach to constructing solutions expres sed through higher analogues of Painlevé transcendents)\; 4) there are co nnections with other constructions\, such as squared eigenfunctions symmet ries and Bäcklund transformations. In the talk\, we consider examples rel ated to the KdV\, Boussinesq and Krichever-Novikov equations and the Volte rra lattice.\n LOCATION:https://researchseminars.org/talk/mmandim/75/ END:VEVENT END:VCALENDAR