Applied Maths Seminar: Nijhoff -- Multidimensional consistency and Lagrangian structures

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

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.)  

http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2010/nijhoff.html