# 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} }

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 $$(1\,{+}\,1)$$
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-dimensional space-time…

## 11 Citations

### Hamiltonian structures for integrable hierarchies of Lagrangian PDEs

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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.…

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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.…

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### Semi-discrete Lagrangian 2-forms and the Toda hierarchy

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We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is an extension of the ideas known by the names ‘Lagrangian multiforms’ and…

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We cast the classical Yang-Baxter equation (CYBE) in a variational context for the first time, by relating it to the theory of Lagrangian multiforms, a framework designed to capture integrability in…

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