2019/06/30 by Matteo Petrera, Mats Vermeeren · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP #msc:37K05 #msc:37K10
paper · pdf · doi:10.1007/s40879-020-00436-7
published as European Journal of Mathematics (2020)
arxiv created 2020/12/16 · arxiv updated 2020/12/17
We investigate the relation between pluri-Lagrangian hierarchies of 2-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in [Petrera, Suris. J. Nonlinear Math. Phys. 24:sup1, 121--145 (2017)] for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural (1+1)-dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. The corresponding multi-time Euler-Lagrange equations coincide with the original system supplied with commuting evolutionary flows induced by the variational symmetries.