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Infinite Analysis Seminar Tokyo
Seminar information archive ～04/22｜Next seminar｜Future seminars 04/23～
| Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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2018/09/25
16:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Nobutaka Nakazono (Aoyama Gakuin University Department of Physics and Mathematics)
Classification of quad-equations on a cuboctahedron (JAPANESE)
Nobutaka Nakazono (Aoyama Gakuin University Department of Physics and Mathematics)
Classification of quad-equations on a cuboctahedron (JAPANESE)
[ Abstract ]
Adelr-Bobenko-Suris (2003, 2009) and Boll (2011) classified quad-equations on a cube using a consistency around a cube. By use of this consistency, we can define integrable two-dimensional partial difference equations called ABS equations. A major example of ABS equation is the lattice modified KdV equation, which is a discrete analogue of the modified KdV equation. It is known that Lax representations and Backlund transformations of ABS equations can be constructed by using the consistency around a cube, and ABS equations can be reduced to differential and difference Painlevé equations via periodically reductions.
In this talk, we show a classification of quad-equations on a cuboctahedron using a consistency around a cuboctahedron and the relation between a resulting partial difference equation and a discrete Painlevé equation.
This work has been done in collaboration with Prof Nalini Joshi (The University of Sydney).
Adelr-Bobenko-Suris (2003, 2009) and Boll (2011) classified quad-equations on a cube using a consistency around a cube. By use of this consistency, we can define integrable two-dimensional partial difference equations called ABS equations. A major example of ABS equation is the lattice modified KdV equation, which is a discrete analogue of the modified KdV equation. It is known that Lax representations and Backlund transformations of ABS equations can be constructed by using the consistency around a cube, and ABS equations can be reduced to differential and difference Painlevé equations via periodically reductions.
In this talk, we show a classification of quad-equations on a cuboctahedron using a consistency around a cuboctahedron and the relation between a resulting partial difference equation and a discrete Painlevé equation.
This work has been done in collaboration with Prof Nalini Joshi (The University of Sydney).
