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  • Letter
  • Open Access

Darboux-Kadomtsev-Petviashvili system as an integrable Chern-Simons multiform theory in infinite dimensional space

João Faria Martins*, Frank W. Nijhoff†, and Daniel Riccombeni‡

  • School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

  • *J.FariaMartins@leeds.ac.uk
  • †frank.nijhoff@gmail.com
  • ‡D.A.Riccombeni@leeds.ac.uk
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Phys. Rev. D 109, L021701 – Published 9 January, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L021701

Abstract

The Darboux-Kadomtsev-Petviashvili system is a universal three-dimensional integrable field theory, which is a generating system for the entire Kadomtsev-Petviashvili hierarchy, and at the same time generalizes the Darboux system, describing orthogonal curvilinear coordinates. In this paper, we establish a hierarchy of Lagrangian multiforms for the Darboux-Kadomtsev-Petviashvili system, derived from a hierarchy of Chern-Simons actions in an infinite-dimensional space of Miwa variables. This provides an integrable variational description of this multidimensionally consistent field theory embedded in infinite dimensional space.

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Phys. Rev. D 109, L021701– Published 9 January, 2024
  • Received 25 May 2023
  • Accepted 13 December 2023
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