Artur Sergyeyev

Integrable systems in higher dimensions: a new perspective

The search for partial differential systems in four independent variables that are integrable in the sense of soliton theory is a problem of longstanding interest, as according to general relativity our spacetime is four-dimensional and for a long time it appeared that such systems are very scarce. We show that this is not really the case. Namely, we will present an explicit effective construction that produces inter alia two infinite families of integrable systems in four independent variables as well as e.g. the first example of a system of this kind with nonisospectral Lax pair which is algebraic, rather than rational, in the spectral parameter.

XXXIX Workshop on Geometric Methods in Physics	19.06–25.06.2022
XI School on Geometry and Physics	27.06–1.07.2022

Event sponsored by:
University of Bialystok