Variational symmetries and Lagrangian multiforms
arXiv:1906.05084 · doi:10.1007/s11005-019-01240-5
Abstract
By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether's theorem to show that every variational symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we provide a systematic method for constructing Lagrangian multiforms for which the closure property and the multiform Euler-Lagrange (EL) equations both hold. We present three examples, including the first known example of a Lagrangian 3-form: a multiform for the Kadomtsev-Petviashvili equation. We also present a new proof of the multiform EL equations for a Lagrangian k-form for arbitrary k.
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Cited by in corpus (15)
- Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy
- Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs
- Lagrangian 3-form structure for the Darboux system and the KP hierarchy
- Multiform description of the AKNS hierarchy and classical r-matrix
- Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies
- Hamiltonian multiform description of an integrable hierarchy
- Lagrangian multiforms on coadjoint orbits for finite-dimensional integrable systems
- Lagrangian multiforms on Lie groups and non-commuting flows
- Hamiltonian structures for integrable hierarchies of Lagrangian PDEs
- Hamiltonian formulation and aspects of integrability of generalised hydrodynamics
- Semi-discrete Lagrangian 2-forms and the Toda hierarchy
- On the Lagrangian multiform structure of the extended lattice Boussinesq system
- On the geometry of Lagrangian one-forms
- Lagrangian multiforms and dispersionless integrable systems
- Lagrangian multiform structure of discrete and semi-discrete KP systems