17 may 2019 -- 13:00
University of Hradec Králové
Abstract.
In this talk we will show how we construct a family of integrable systems as reductions of the dressing chain, described in its Lotka-Volterra form. For any two non-negative integers $k,n$ satisfying $n\geq 2k+1$ we obtain a Lotka-Volterra system which on the one hand is a reduction of the dressing chain of $2m+1$ variables and on the other hand is a deformation of an integrable reduction of the $2m+1$-dimensional Bogoyavlenskij-Itoh system, where $m=n-k-1$. We will show that the systems obtained are both Liouville and non-commutative integrable. For the particular case $k=0$ we also construct a family of discretizations of the obtained integrable systems, including their Kahan discretization, and we show that these discretizzations are also Liouville and superintegrable.