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SUMMARY:The singularity structure of the discrete KdV and mKdV equations
DTSTART;VALUE=DATE-TIME:20230622T071500Z
DTEND;VALUE=DATE-TIME:20230622T074500Z
DTSTAMP;VALUE=DATE-TIME:20260905T173912Z
UID:indico-contribution-0-19@cern.ch
DESCRIPTION:Speakers: Prof. WILLOX\, Ralph (the University of Tokyo)\nAlth
 ough the notion of singularity confinement was first introduced for the di
 screte KdV (dKdV) equation\, as of yet there is still no rigorous definiti
 on of the notion of `confinement' for lattice equations. In fact\, somewha
 t ironically\, it has taken nearly 30 years before an exhaustive study of 
 the singularities of the dKdV equation finally revealed their intriguing p
 roperties and the full richness of the singularity structures they produce
 . \nIn this talk I will explain the basic classification of singularities 
 for the dKdV and mKdV equations\, which involves a novel `strip-like' type
  of singularity. These strips or bands can interact with the singularities
  of other types\, producing singularity patterns of increasing complexity.
  Moreover\, I will show that the interaction of these singularities with a
  particular type of singularity can be described using a special symbolic 
 dynamics which turns out to be equivalent to the Takahashi-Satsuma Box&Bal
 l dynamics.\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=1
 9&sessionId=0&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=19&sessionId
 =0&confId=67
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BEGIN:VEVENT
SUMMARY:Full deautonomisation by singularity confinement as an integrabili
 ty test
DTSTART;VALUE=DATE-TIME:20230622T074500Z
DTEND;VALUE=DATE-TIME:20230622T081500Z
DTSTAMP;VALUE=DATE-TIME:20260905T173912Z
UID:indico-contribution-0-18@cern.ch
DESCRIPTION:Speakers: Dr. STOKES\, Alexander (The University of Tokyo)\nSi
 nce its introduction\, the method of full deautonomisation by singularity 
 confinement has proved a strikingly effective way of detecting the dynamic
 al degrees of birational mappings of the plane.\nThis method is based on a
  conjectured link between two a priori unrelated notions: firstly the dyna
 mical degree of the mapping and secondly the evolution of parameters requi
 red for its singularity structure to remain unchanged under a sufficiently
  general deautonomisation.\nIn this talk we will present a proof of this c
 onjectured correspondence for a large class of birational mappings of the 
 plane via the spaces of initial conditions for their deautonomised version
 s.\nWe show that even for non-integrable mappings in this class\, the surf
 aces forming these spaces have effective anticanonical divisors and one ca
 n define a kind of period mapping\, which provides a bridge between the ev
 olution of coefficients in the deautonomised mapping and the induced dynam
 ics on the Picard lattice which encode the dynamical degree.\nWe will illu
 strate the method in some examples and also discuss connections to the the
 ory of rational surfaces associated with root systems of indefinite type.\
 n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=18&sessionId=
 0&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=18&sessionId
 =0&confId=67
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BEGIN:VEVENT
SUMMARY:Singularity analysis and bilinear approach to some Bogoyavlensky d
 ifferential difference equations
DTSTART;VALUE=DATE-TIME:20230622T081500Z
DTEND;VALUE=DATE-TIME:20230622T084500Z
DTSTAMP;VALUE=DATE-TIME:20260905T173912Z
UID:indico-contribution-0-36@cern.ch
DESCRIPTION:Speakers: Dr. CARSTEA\, Adrian Stefan (Institute of Physics an
 d Nuclear Engineering\, Dept of Theoretica Physics\, Magurele\, Bucharest 
 077125\, Romania)\nWe discuss singularity analysis and bilinear integrabil
 ity of four\nBogoyavlensky differential-difference equations. Three of the
 m are\ncompletely integrable and the fourth is\, to our knowledge\, a new 
 one.\nBlending the singularity confinement with Painlevé property reveals
 \nstrictly confining and anticonfining (weakly confining) singularity pat-
 \nterns. The strictly confining patterns are useful because\nthey provide 
 different representations using tau functions and a possible extension of 
 the so called "express method" for testing integrability. For the new prop
 osed equation we get also the bilinear form\nand multisoliton solution\, b
 eing a good candidate for a new integrable\nsystem. In addition\, using bi
 linear formalism we recover the integrable\ntime-discretisations of the fi
 rst three systems.\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?cont
 ribId=36&sessionId=0&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=36&sessionId
 =0&confId=67
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