Speaker: Pavlos Xenitidis (Liverpool Hope University, UK)

Title: Noncommutative discrete KdV equations, their symmetries and reductions

Date and time:  21.05.2025, 17:00 (GMT +03:00)

Abstract: Employing the Lax pairs of the discrete noncommutative Hirota's Korteweg-de Vries (KdV) and the potential KdV equations, we derive differential-difference equations consistent with these equations which play the role of generalised symmetries of the latter. Miura transformations map them to a noncommutative modified Volterra equation and its master symmetry are given. The use of the symmetries for the reduction of the potential KdV equation is demonstrated and the reductions to a noncommutative discrete Painleve equation and a system of partial differential equations generalising the Ernst equation and the Neugebauer-Kramer involution are presented. A Darboux and an auto-Backlund transformation for the Hirota KdV are presented and their relation to the noncommutative Yang-Baxter map is given.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com