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Lagrangian multiforms and multidimensional consistency

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arxiv 0903.4086 v2 pith:Z3VWYW5H submitted 2009-03-24 nlin.SI

Sarah Lobb , Frank Nijhoff This is my paper · ORCID
classification nlin.SI
keywords lagrangianlatticeconsistencymultidimensionalmultiformsbasisclassclosure
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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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  1. Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations

    nlin.SI 2025-01 conditional novelty 7.0 of 10

    Trident Lagrangian 2-forms with integer-valued branch-tracking fields have corner equations equivalent to the ABS quad equations and restore almost-closure.

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