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arXiv · 2011.04543

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

Duncan Sleigh·Frank Nijhoff·Vincent Caudrelier
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Abstract

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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Duncan Sleigh, Frank Nijhoff, Vincent Caudrelier. 2020-11-09. Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy. https://doi.org/10.1093/imrn%2Frnab288

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