• DOI:10.1007/s40879-020-00436-7
• Corpus ID: 184487635

Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

@article{Petrera2019VariationalSA,
  title={Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs},
  author={Matteo Petrera and Mats Vermeeren},
  journal={European Journal of Mathematics},
  year={2019}
}

• M. Petrera, Mats Vermeeren
• Published 1 June 2019
• Mathematics
• European Journal of Mathematics

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 and Suris (Nonlinear Math. Phys. 24(suppl. 1):121–145, 2017) for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural $$(1\,{+}\,1)$$

(
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.