Lagrangian multiforms and dispersionless integrable systems

Abstract

We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the context of Gibbons-Tsarev equations governing hydrodynamic reductions of heavenly type equations in 4D.

25 pages. v2: extended introduction and other minor improvements and corrections

References in corpus (21)

• On integrability of (2+1)-dimensional quasilinear systems
• Gurevich-Zybin system
• Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability
• Lagrangian multiforms and multidimensional consistency
• The Lagrangian of a Self-Dual Gravitational Field as a Limit of the SDYM Lagrangian
• Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms
• Discrete-time Calogero-Moser system and Lagrangian 1-form structure
• Hydrodynamic reductions of the heavenly equation
• What is integrability of discrete variational systems?
• On the Lagrangian structure of integrable hierarchies
• Veronese webs and nonlinear PDEs
• Variational symmetries and pluri-Lagrangian systems in classical mechanics
• Variational symmetries and Lagrangian multiforms
• Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs
• Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations
• Lagrangian 3-form structure for the Darboux system and the KP hierarchy
• Second-order PDEs in 3D with Einstein-Weyl conformal structure
• Lagrangian multiforms on coadjoint orbits for finite-dimensional integrable systems
• Second-order PDEs in 4D with half-flat conformal structure
• Discrete Lagrangian Multiforms for ABS Equations II: Tetrahedron and Octahedron Equations
• Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations