

Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
January 14, 2015 14:00, Moscow, Lomonosov Moscow State University, Steklov Mathematical Institute of RAS






Darboux transformations and integrable differential–difference
equations associated with Kac–Moody Lie algebras
A. V. Mikhailov^{ab} ^{a} University of Leeds, School of Mathematics
^{b} Skolkovo Institute of Science and Technology

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Abstract:
It is well known that with every Kac–Moody Lie algebra one can
associate an integrable two dimensional Toda type system. In paticular
the sinhGordon equation corresponds to the algebra $A_1^{(1)}$,
the Tzitzeica equation to $A_2^{(2)}$, the usual periodic Toda lattice to
$A_n^{(1)}$, etc. In our work we construct integrable chains of
B"acklund transformations for Toda type systems associated with
the classical families of Kac–Moody algebras and derive Darboux
transformations for the corresponding Lax operators.
We also discuss integrable finite difference systems corresponding
to the Bianchi permutability of the Bäcklund transformations.
Language: English

