Variational symmetries and Lagrangian multiforms
Mathematical Physics
2020-05-15 v3 math.MP
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.
Keywords
Cite
@article{arxiv.1906.05084,
title = {Variational symmetries and Lagrangian multiforms},
author = {D. G. Sleigh and F. W. Nijhoff and V. Caudrelier},
journal= {arXiv preprint arXiv:1906.05084},
year = {2020}
}