# Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies

@inproceedings{Caudrelier2022ClassicalYE, title={Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies}, author={Vincent Caudrelier and Matteo Stoppato and Beno{\^i}t Vicedo}, year={2022} }

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 a variational fashion. This provides a significant connection between Lagrangian multiforms and the CYBE, one of the most fundamental concepts of integrable systems. This is achieved by introducing a generating Lagrangian multiform which depends on a skew-symmetric classical r-matrix with spectral…

## 2 Citations

### Lagrangian multiforms on Lie groups and non-commuting flows

- Mathematics
- 2022

We describe a variational framework for non-commuting ﬂows, extending the theories of Lagrangian multiforms and pluri-Lagrangian systems, which have gained prominence in recent years as a variational…

### Lax equations for relativistic GL(NM,C) Gaudin models on elliptic curve

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

We describe the most general GL NM classical elliptic finite-dimensional integrable system, which Lax matrix has n simple poles on elliptic curve. For M = 1 it reproduces the classical inhomogeneous…

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