Trident Lagrangian 2-forms with integer-valued branch-tracking fields have corner equations equivalent to the ABS quad equations and restore almost-closure.
Lagrangian multiforms and multidimensional consistency
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abstract
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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Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations
Trident Lagrangian 2-forms with integer-valued branch-tracking fields have corner equations equivalent to the ABS quad equations and restore almost-closure.