Trident Lagrangian 2-forms with integer-valued branch-tracking fields have corner equations equivalent to the ABS quad equations and restore almost-closure.
Lagrangian 3-form structure for the Darboux system and the KP hierarchy
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A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the entire Kadomtsev-Petviashvili (KP) hierarchy in terms so-called Miwa variables. Thus, in providing a Lagrangian description of this multidimensionally consistent system amounts to a new Lagrangian 3-form structure for the continuous KP system. A generalisation to the matrix (also known as non-Abelian) KP system is discussed.
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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.