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BIMSA Integrable Systems Seminar
The Elliptic lattice KdV system: a curious discrete integrable system
The Elliptic lattice KdV system: a curious discrete integrable system
演讲者
Frank Nijhoff
时间
2025年04月01日 16:00 至 17:00
地点
A6-101
线上
Zoom 873 9209 0711
(BIMSA)
摘要
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