BIMSA > BIMSA Integrable Systems Seminar The Elliptic lattice KdV system: a curious discrete integrable system
The Elliptic lattice KdV system: a curious discrete integrable system
Organizers
Andrii Liashyk , Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Frank Nijhoff
Time
Tuesday, April 1, 2025 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711 (BIMSA)
Abstract
The elliptic lattice KdV was introduced in 2003 as a system that generalises the lattice potential KdV equation. It is a rather complicated system for 3 components which contains an elliptic curve in the fixed parameters (in addition to the lattice parameters). It was constructed on the basis of a `direct linearisation scheme' with an elliptic Cauchy kernel. In the talk I will highlight some newly discovered aspects: a reformulation in terms of a 2-component multiquartic system, an associated elliptic Yang-Baxter map, aan associated system of 2x2 matrix equations and and a 6-component elliptic generalisation of the Ernst equations which forms the `generating PDE system' for the related continuous hierarchy of integrable PDEs. (This work is in collaboration with Cheng Zhang and Da-jun Zhang