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SUMMARY:V.E. Adler (Landau Institute for Theoretical Physics)
DTSTART:20240418T110000Z
DTEND:20240418T120000Z
DTSTAMP:20260423T005822Z
UID:mmandim/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/74/"
 >Negative symmetries: properties and applications</a>\nby V.E. Adler (Land
 au Institute for Theoretical Physics) as part of Mathematical models and i
 ntegration methods\n\n\nAbstract\nOne of the definitions of negative symme
 try of an integrable equation is given by the formula $u_t=(R-a)^{-1}(0)$ 
 where $R$ is the recursion operator and $a$ is a parameter. This extension
  of symmetry algebra is of interest from different points of view: 1) nega
 tive symmetry can be interesting as an independent equation\; 2) it contai
 ns information about the entire integrable hierarchy\, since the expansion
  in parameter a serves as a generating function for higher symmetries\; 3)
  there are applications in the problem of constructing finite-dimensional 
 reductions\, especially in combination with classical symmetries (which pr
 ovides an approach to constructing solutions expressed through higher anal
 ogues of Painlevé transcendents)\; 4) there are connections with other co
 nstructions\, such as squared eigenfunctions symmetries and Bäcklund tran
 sformations. In the talk\, we consider examples related to the KdV\, Bouss
 inesq and Krichever-Novikov equations and the Volterra lattice.\n
LOCATION:https://researchseminars.org/talk/mmandim/74/
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