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.

Some referee's comments taken into account and some misprints corrected

References in corpus (2)

• A Variational Approach to Lax Representations
• Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems

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