Cluster maps, discrete Hirota reductions and the lattice KdV equation

Theodoros Kouloukas. University of Kent. Virtual seminar.

Plane wave type reductions of the discrete Hirota equation are associated with periodic reductions of integrable lattice equation. On the other hand, discrete Hirota reductions are particular examples of cluster maps, which arise from cluster mutations of periodic quivers. In this talk, we focus on a particular class of Hirota reductions associated with the (N,M) periodic reductions of the lattice KdV equation. We will demonstrate the integrability in the Liouville sense of the lattice KdV periodic reductions and the corresponding U-systems of the discrete Hirota reductions using the properties of the underlying cluster algebra structure.

This is joint work with Andy Hone. The talk is based on the paper Discrete Hirota reductions associated with the lattice KdV equation, J. Phys. A: Math.Theor. 53, 364002 (2020).