Variational symmetries and Lagrangian multiforms

2019/06/30 by D. G. Sleigh, F. W. Nijhoff, V. Caudrelier · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf · doi:10.1007/s11005-019-01240-5

published as Lett Math Phys 110, 805-826 (2020)

arxiv created 2020/05/14 · arxiv updated 2020/05/15

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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