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International conference "Geometrical Methods in Mathematical Physics"
December 16, 2011 16:45–17:30, Moscow, Lomonosov Moscow State University
 


Cartan matrices and integrable lattice Toda field equations

I. T. Habibullin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
Supplementary materials:
Adobe PDF 294.5 Kb

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Abstract: Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_{2},B_{2},C_{2},G_{2}$ the complete sets of integrals in both directions are found.
For the simple Lie algebras of the classical series $A_{N},B_{N},C_{N}$ and affine algebras of series $D_{N}^{(2)}$ the corresponding systems are supplied with the Lax representation.


References.
[1] Ismagil Habibullin, Kostyantyn Zheltukhin and Marina Yangubaeva, Cartan matrices
and integrable lattice Toda field equations, J. Phys. A: Math. Theor. 44 (2011) 465202
(20pp).
[2] Ismagil Habibullin, Rustem N. Garifullin, Affine Lie algebras and integrable Toda field
equations on discrete space-time, arXiv:1109.1689 (2011).

Supplementary materials: gmmp2011_ihabibullin.pdf (294.5 Kb)

Language: English
 
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