Seminars: A. V. Mikhailov, Darboux transformations and integrable differential--difference equations associated with Kac--Moody Lie algebras

SEMINARS


Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) 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
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 sinh-Gordon 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