Doliwa A. Non-commutative integrable discrete systems of a geometric origin, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)

From Geometry of Differential Equations
Jump to: navigation, search

Speaker: Adam Doliwa

Title: Non-commutative integrable discrete systems of a geometric origin

Abstract:
We investigate periodic reductions of Desargues maps, which lead to novel integrable multicomponent lattice systems being non-commutative, non-isospectral, and non-autonomous analogues of the modified Gel'fand-Dikii hierarchy. We show directly multidimensional consistency of the equations, and we present the corresponding systems of Lax pairs. We also provide a construction of related noncommutative rational maps which satisfy the Yang-Baxter property.

Slides: Doliwa A. Non-commutative integrable discrete systems of a geometric origin (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).pdf