The Elliptic lattice KdV system: a curious discrete integrable system

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.)

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.