# Hamiltonian multiform description of an integrable hierarchy

@article{Caudrelier2020HamiltonianMD, title={Hamiltonian multiform description of an integrable hierarchy}, author={Vincent Caudrelier and Matteo Stoppato}, journal={arXiv: Mathematical Physics}, year={2020} }

Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of integrability, and by results of the authors on the role of covariant Hamiltonian formalism for integrable field theories, we propose the notion of Hamiltonian multiforms for integrable $1+1$-dimensional field theories. They provide the Hamiltonian counterpart of Lagrangian multiforms and encapsulate in a single object an arbitrary number of flows within an integrable hierarchy. For a given hierarchy…

## 5 Citations

Multiform description of the AKNS hierarchy and classical r-matrix

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2021

In recent years, new properties of space-time duality in the Hamiltonian formalism of certain integrable classical field theories have been discovered and have led to their reformulation using ideas…

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- Mathematics
- 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…

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…

Hamiltonian structures for integrable hierarchies of Lagrangian PDEs

- MathematicsOpen Communications in Nonlinear Mathematical Physics
- 2021

Many integrable hierarchies of differential equations allow a variational
description, called a Lagrangian multiform or a pluri-Lagrangian structure. The
fundamental object in this theory is not a…

On the Zakharov–Mikhailov action: $$4\hbox {d}$$ Chern–Simons origin and covariant Poisson algebra of the Lax connection

- Mathematics
- 2020

We derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory. This $2$d action is known to produce as equations of motion the flatness condition of a large class of Lax connections of…

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