Variational symmetries and Lagrangian multiforms
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) both hold. We present three examples, including the first known example of a continuous 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.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- November 2019
- DOI:
- 10.1007/s11005-019-01240-5
- arXiv:
- arXiv:1906.05084
- Bibcode:
- 2019LMaPh.110..805S
- Keywords:
-
- Integrable systems;
- Variational principle;
- Variational symmetries;
- Lagrangian multiforms;
- Mathematical Physics
- E-Print:
- Lett Math Phys 110, 805-826 (2020)