BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Integral preserving discretization of 2D Toda lattice
DTSTART;VALUE=DATE-TIME:20230621T074500Z
DTEND;VALUE=DATE-TIME:20230621T081500Z
DTSTAMP;VALUE=DATE-TIME:20260430T223309Z
UID:indico-contribution-45@cern.ch
DESCRIPTION:Speakers: Dr. SMIRNOV\, Sergey (Lomonosov Moscow State Univers
 ity)\n2D-Toda lattices corresponding to the Cartan matrices of simple Lie 
 algebras are known to be Darboux integrable\, i.e. they admit complete fam
 ilies of essentially independent characteristic integrals. During the last
  three decades various discrete analogs of these systems were obtained. In
  2011 Habibullin proposed a systematic way to discretize 2D-Toda lattices.
  His approach was based on the \nidea to look for semi-discrete systems su
 ch that they have the same characteristic integrals as their continuous an
 alogs. Careful analysis of the systems corresponding to the Cartan matrice
 s of the rank 2 allowed Habibullin and his collaborators to introduce semi
 -discrete and purely discrete analogs of 2D-Toda lattices and to conjectur
 e that they are Darboux integrable for Cartan matrices \nof arbitrary rank
 . After that some partial results on Darboux integrability of these system
 s were obtained\, but the general claim remained unproved.\n\nWe prove tha
 t if function I is a y-integral of 2D-Toda lattice corresponding to some C
 artan matrix\, then this function is an n-integral of its semi-discrete an
 alog. This implies the existence of a complete family of n-integrals for e
 ach of these systems. We use the concept of characteristic algebra to prov
 e that these systems admit complete families of characteristic x-integrals
  as well.\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=45&
 sessionId=5&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=45&sessionId
 =5&confId=67
END:VEVENT
END:VCALENDAR