Lecturer in Mathematics, Dr Pavlos Xenitidis, from the School of Mathematics, Statistics and Actuarial Science (SMSAS) at the University of Kent, spoke at the Ninth International Workshop on ‘Group Analysis of Differential Equations and Integrable Systems’, in Larnaca, Cyprus, earlier this month (June 2018).
Pavlos delivered a talk titled, ‘Deautonomization of integrable difference equations’ at the Workshop organised by the Department of Mathematics and Statistics at the University of Cyprus and the Department of Mathematical Physics from the Institute of Mathematics at the National Academy of Sciences of Ukraine.
Abstract:
Integrability conditions for difference equations can be used not only to check the integrability of a given equation but also to compute its generalised symmetries and derive conservation laws. In this talk we explore one more application of these conditions: the construction of integrable non-autonomous equations. We demonstrate how the integrability conditions can be used to deautonomize a given autonomous equation and apply this procedure to a certain family of equations defined on an elementary quadrilateral of the Z2 lattice. In particular we show that all the non-autonomous equations we find are related via Miura transformations to the same integrable two-quad autonomous equation. Finally we prove the integrability of the latter equation by generating an infinite hierarchy of its symmetries using a local master symmetry.
Click here for more information about the Workshop.
Dr Pavlos Xenitidis
Lecturer in Mathematics
Pavlos is a Lecturer in Mathematics and is the Seminar Organiser for the Integrable Systems and Mathematical Physics Seminars at Kent. His research interests include the classification of integrable systems, Painlevé equations, discretization of differential equations, symmetries, conservation laws and integrability tests.