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Applied Mathematics Seminar
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Frank Nijhoff
Department of Applied Mathematics, University of Leeds, UK

Multidimensional consistency and Lagrangian structures

Wednesday 31st March 14:05-14:55pm, New Law School Seminar 030 (Building F10).

Multidimensional consistency is nowadays considered to be one of the hallmarks of integrable equations on the lattice, i.e. partial difference equations in two or more dimensions. However, it also applies to certain families of continuous equations, namely partial differential equations associated with integrable hierarchies. The new notion of Lagrangian multiform structures, introduced by Lobb and Nijhoff in 2009, is a manifestation of multidimensional consistency on the level of the Lagrange structures and least-action principles. In the talk, I will describe this property and show how it emerges in various examples of discrete and continuous equations. (This is work in collaboration with Sarah Lobb and Pavlos Xenitidis.)