New Variational Principle for Integrable Systems
by Professor Frank W Nijhoff
Abstract: Many integrable systems are characterized by the property of multidimensional consistency,i.e. the phenomenon that the relevant equation can be embedded in a higher-dimensional space-time in a consistent way.This could happen for differential equations admitting hierarchies of compatible equations, or for discrete systems on lattices which can be covariantly embedded in multidimensional discrete space-time. Recently [Lobb&Nijhoff,2009] a Lagrangian formulation was proposed for this phenomenon based on the idea of "Lagrangian multiforms". We discuss the corresponding variational principle and present several examples in 1 and 2 dimensions.
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