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arXiv · 2305.03182

The Darboux-KP system as an integrable Chern-Simons multiform theory in infinite dimensional space

Joao Faria Martins·Frank W Nijhoff·Daniel Riccombeni
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Abstract

In a previous paper by one of the authors, a Lagrangian 3-form structure was established for a generalised Darboux system, originally describing orthogonal curvilinear coordinate systems, which encodes the Kadomtsev-Petviashvili (KP) hierarchy. Here a hierarchy of Lagrangian multiforms is established for the same system, viewed as a hierarchy of Chern-Simons actions in an infinite-dimensional space of Miwa variables, constituting the variational form of a universal 3D integrable system embedded in this infinite-dimensional space.

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Joao Faria Martins, Frank W Nijhoff, Daniel Riccombeni. 2023-05-04. The Darboux-KP system as an integrable Chern-Simons multiform theory in infinite dimensional space. https://arxiv.org/abs/2305.03182

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