Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy
Exactly Solvable and Integrable Systems
2025-04-25 v3 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2011.04543,
title = {Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy},
author = {Duncan Sleigh and Frank Nijhoff and Vincent Caudrelier},
journal= {arXiv preprint arXiv:2011.04543},
year = {2025}
}
Comments
26 pages. Authors' version of the accepted paper in Int. Math. Res. Not. Accessible online from https://doi.org/10.1093/imrn/rnab288