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. Published by the American Physical Society 2024
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