• Corpus ID: 246063549

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

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

Lagrangian multiforms on Lie groups and non-commuting flows

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

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



Hamiltonian multiform description of an integrable hierarchy

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

Multiform description of the AKNS hierarchy and classical r-matrix

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

Continuum limits of pluri-Lagrangian systems

  • Mats Vermeeren
  • Mathematics, Computer Science
    Journal of Integrable Systems
  • 2019
A continuum limit procedure for pluri-Lagrangian systems, where the lattice parameters are interpreted as Miwa variables, describing a particular embedding in continuous multi-time of the mesh on which the discrete system lives.

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

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

Assembling integrable σ-models as affine Gaudin models

A bstractWe explain how to obtain new classical integrable field theories by assembling two affine Gaudin models into a single one. We show that the resulting affine Gaudin model depends on a

On Integrable Field Theories as Dihedral Affine Gaudin Models

  • B. Vicedo
  • Mathematics
    International Mathematics Research Notices
  • 2018
We introduce the notion of a classical dihedral affine Gaudin model, associated with an untwisted affine Kac–Moody algebra $\widetilde{\mathfrak{g}}$ equipped with an action of the dihedral group