Stationary systems and non-autonomous soliton hierarchies.
Prof. Błażej Szablikowski, ISQI

Date, Time
27.03, 15:00 - 16:00

Location
hybrid meetnig (room 16), link (MSTeams) >>>

I will present recent results of joint work with Maciej Błaszak (UAM) and Krzysztof Marciniak (Linköping University). I will try to make the lecture accessible to people who are not experts in the field of integrable systems, so I will focus on an introduction to the topic and omit technical details.

Since the classical works of Novikov et al. there has been a tremendous amount of research devoted to connections between soliton hierarchies and their integrable finite-dimensional reductions, which was mainly focused on stationary flows. Recently, we have revisited this idea in a novel, systematic way. We investigated not only stationary flows but the so-called stationary systems, by which we mean a stationary flow together with all lower flows from the hierarchy, that is finite dimensional systems of evolutionary equations. As result, we were able to show that in the case of the particular soliton hierarchies the related stationary systems can be represented as a classical separable Stäckel systems.

It turns out that non-autonomous soliton hierarchies are almost completely unexplored. Another result that we recently obtained is the introduction of a formalism for the systematic construction of integrable non-autonomous deformations of soliton hierarchies. The theory is formulated as an initial value problem for Frobenius integrability conditions on associated Lie algebras.