Lagrangian 3-form structure for the Darboux system and the KP hierarchy

Abstract

A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the entire Kadomtsev-Petviashvili (KP) hierarchy in terms so-called Miwa variables. Thus, in providing a Lagrangian description of this multidimensionally consistent system amounts to a new Lagrangian 3-form structure for the continuous KP system. A generalisation to the matrix (also known as non-Abelian) KP system is discussed.

arXiv commentSome referee's comments taken into account and some misprints corrected

References in corpus (18)

• Multidimensional Quadrilateral Lattices are Integrable
• Lattice and q-difference Darboux-Zakharov-Manakov systems via $\bar{\partial }$-dressing method
• Lagrangian multiforms and multidimensional consistency
• On a Schwarzian PDE associated with the KdV Hierarchy
• Direct linearising transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations
• Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets
• Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms
• Discrete-time Calogero-Moser system and Lagrangian 1-form structure
• What is integrability of discrete variational systems?
• A Variational Approach to Lax Representations
• On the Lagrangian structure of integrable hierarchies
• Linear integral equations, infinite matrices, and soliton hierarchies
• Variational symmetries and Lagrangian multiforms
• The KP Hierarchy in Miwa Coordinates
• Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy
• Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems
• Generalized hyperbolic Ernst equations for an Einstein-Maxwell-Weyl field
• On $\tau$-function of conjugate nets

Cited by in corpus (6)

• Lagrangian multiforms on coadjoint orbits for finite-dimensional integrable systems
• On the Lagrangian multiform structure of the extended lattice Boussinesq system
• Lagrangian multiform structure of discrete and semi-discrete KP systems
• Lagrangian multiforms and dispersionless integrable systems
• On the geometry of Lagrangian one-forms
• Lagrangian Multiform for Cyclotomic Gaudin Models