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Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy

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arxiv 2011.04543 v3 pith:M3ALDZCY submitted 2020-11-09 nlin.SI math-phmath.MP

Duncan Sleigh , Frank Nijhoff , Vincent Caudrelier This is my paper · ORCID
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keywords hierarchylagrangiangelfand-dickeyhierarchieskadomtsev-petviashvilimultiformmultiformsamongst
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We present, for the first time, a Lagrangian multiform for the complete Kadomtsev-Petviashvili (KP) hierarchy -- a single variational object that generates the whole hierarchy and encapsulates its integrability. By performing a reduction on this Lagrangian multiform, we also obtain Lagrangian multiforms for the Gelfand-Dickey hierarchy of hierarchies, comprising, amongst others, the Korteweg-de Vries and Boussinesq hierarchies.

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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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