Lagrangian multiforms and multidimensional consistency

Details Lagrangian multiforms and multidimensional consistency Lagrangian multiforms and multidimensional consistency

2009-03-24

arxiv.org/abs/0903.4086v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, typos corrected, submitted to the special issue on "Symmetries and Integrability of Difference Equations" of J. Phys

Scientific paper

We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis of this property we formulate a Lagrangian description for such systems in terms of Lagrangian multiforms. We discuss the connection of this formalism with the notion of multidimensional consistency, and the role of the lattice from the point of view of the relevant variational principle.

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