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SUMMARY:tau function\, vertex operator and linearization scheme associated
  with Lamé function
DTSTART;VALUE=DATE-TIME:20230621T103000Z
DTEND;VALUE=DATE-TIME:20230621T110000Z
DTSTAMP;VALUE=DATE-TIME:20260404T013743Z
UID:indico-contribution-7-31@cern.ch
DESCRIPTION:Speakers: Prof. ZHANG\, Da-jun (Shanghai University)\nThe talk
  contains two parts. In the first part I will describe a bilinear framewor
 k for elliptic soliton solutions (which are composed by the Lamé-type pla
 ne wave factors and expressed using Weierstrass functions). The framework 
 includes tau functions in Hirota’s form\, vertex operators to generate s
 uch tau functions and the associated bilinear identities. These are introd
 uced in detail for the KdV equation and sketched for the KP hierarchy. The
  second part I will report an elliptic direct linearisation scheme associa
 ted with discrete Lamé-type plane wave factors. This scheme allows us to 
 have lattice KP equations and lattice Boussinesq equations that have ellip
 tic soliton solutions. In both continuous can discrete cases\, the so-call
 ed elliptic N-th roots of unity are needed to define plane wave factors an
 d implement reductions. This talk is based on a joint work with Xing Li (a
 rxiv: 2204.01240) and a joint work with Frank Nijhoff and Yingying Sun (19
 09.02948).\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=31
 &sessionId=7&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=31&sessionId
 =7&confId=67
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BEGIN:VEVENT
SUMMARY:Lagrangian multiforms and discrete and semi-discrete KP systems
DTSTART;VALUE=DATE-TIME:20230621T093000Z
DTEND;VALUE=DATE-TIME:20230621T100000Z
DTSTAMP;VALUE=DATE-TIME:20260404T013743Z
UID:indico-contribution-7-15@cern.ch
DESCRIPTION:Speakers: Prof. NIJHOFF\, Frank (University of Leeds)\nRecentl
 y I presented a Lagrangian 3-form structure for a generalised Darboux syst
 em. The original Darboux system arose in connection with the theory of con
 jugate nets for systems of orthogonal curvilinear coordinates. The general
 ised system\, in which the relevant fields are labelled by continuous para
 meters which can be associated with lattice parameters of an underlying \n
 3-dimensional integrable discrete system\, amounts to a presentation of th
 e KP \nhierarchy in terms of Miwa variables\, and can be thought of as a "
 generating PDE" system for that hierarchy. In connection with this result\
 , the case of Lagrangian multiforms for fully discrete and semi-discrete K
 P type systems was left open\, except in the case of the bilinear form of 
 the discrete KP equation \nthe multiform structure of which was establishe
 d in 2009. In contrast\, I will present 3-form structures for the actual n
 onlinear forms of the (potential) discrete and semi-discrete KP equations.
 \n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?contribId=15&sessionId
 =7&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=15&sessionId
 =7&confId=67
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BEGIN:VEVENT
SUMMARY:Multiform Structures of Ordinary Difference Equations Satisfying A
 ddition Formulae
DTSTART;VALUE=DATE-TIME:20230621T100000Z
DTEND;VALUE=DATE-TIME:20230621T103000Z
DTSTAMP;VALUE=DATE-TIME:20260404T013743Z
UID:indico-contribution-7-43@cern.ch
DESCRIPTION:Speakers: Mr. RICHARDSON\, Jacob (University of Leeds)\nIn aim
 ing to find simple nonlinear Lagrangian 1-forms that exhibit all the relev
 ant features of a multiform structure\, we investigate Lagrange structures
  arising from addition formulae. This results in non-quadratic Lagrangians
  and commuting maps with discrete and continuous interpolation flows. We d
 iscuss the relationship to integrable quad equations and applications to q
 uantum propagators.\n\nhttp://indico.fuw.edu.pl/contributionDisplay.py?con
 tribId=43&sessionId=7&confId=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=43&sessionId
 =7&confId=67
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