Display Abstract

Title Lax pairs and spectral curves for Somos sequences

Name Andrew Hone
Country England
Email anwh@kent.ac.uk
Submit Time 2010-02-27 02:39:13
Special Session 66: Discrete Integrable Systems
Somos sequences are integer sequences generated by bilinear difference equations. The aim of this talk is to explain how these bilinear recurrences are related to maps of QRT type and their higher order analogues. In general, an arbitrary bilinear recurrence of this kind does not correspond to an integrable map. However, all known integrable cases can be obtained as reductions of discrete KP (the Hirota-Miwa equation) or discrete BKP (Miwa's equation), and this leads to Lax pairs and spectral curves associated to Somos sequences.