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SUMMARY:Degree growth of some lattice equations defined on  a 3x3 stencil
DTSTART;VALUE=DATE-TIME:20230622T100000Z
DTEND;VALUE=DATE-TIME:20230622T103000Z
DTSTAMP;VALUE=DATE-TIME:20260408T141317Z
UID:indico-contribution-60@cern.ch
DESCRIPTION:Speakers: Prof. HIETARINTA\, Jarmo (University of Turku)\nWe s
 tudy the growth of complexity\, or degree growth\, of one-component\nlatti
 ce equations defined on a 3x3 stencil. The 2x2 case was discussed\nin a pr
 evious talk by T. Mase.  The equations studied here include two\n7-point e
 quations in Hirota bilinear form as well as 9-point\nBoussinesq equations 
 of regular\, modified and Schwarzian type. \nThe initial values are given 
 on a staircase or on a corner configuration and\ndepend linearly or ration
 ally on a special variable x\, and we count\nthe degree in x of the iterat
 es. Known integrable cases have linear\ngrowth if only one initial values 
 contains x\, and quadratic growth if\nall initial values contain x. Even a
  small deformation of an\nintegrable equation changes the degree growth to
  become exponential\,\nbecause the deformation will change factorization p
 roperties and\nthereby prevent cancellations. The simplest case in which o
 nly one initial\nvalue contains x is sufficient to differentiate between i
 ntegrable\nand non-integrable equations.\n\nhttp://indico.fuw.edu.pl/contr
 ibutionDisplay.py?contribId=60&sessionId=2&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=60&sessionId
 =2&confId=67
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