A variational approach to Lax representations

@article{Sleigh2018AVA,
  title={A variational approach to Lax representations},
  author={Duncan Sleigh and Frank W. Nijhoff and Vincent Caudrelier},
  journal={Journal of Geometry and Physics},
  year={2018}
}
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13 Citations
Background Citations
6
Methods Citations
2

13 Citations

Variational symmetries and Lagrangian multiforms

  • Duncan SleighFrank NijhoffVincent Caudrelier
  • Mathematics
    Letters in Mathematical Physics
  • 2019
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.…

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…

Hamiltonian structures for integrable hierarchies of Lagrangian PDEs

  • Mats Vermeeren
  • Mathematics
    Open 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…

Lagrangian 3-form structure for the Darboux system and the KP hierarchy

  • F. Nijhoff
  • Computer Science
    Letters in Mathematical Physics
  • 2023
A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems for the continuous Kadomtsev–Petviashvili (KP) hierarchy.

Lagrangian multiforms on Lie groups and non-commuting flows

Semi-discrete Lagrangian 2-forms and the Toda hierarchy

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…

A connection between the classical r-matrix formalism and covariant Hamiltonian field theory

Lagrangian Multiforms for Kadomtsev–Petviashvili (KP) and the Gelfand–Dickey Hierarchy

We present, for the first time, a Lagrangian multiform for the complete Kadomtsev–Petviashvili hierarchy—a single variational object that generates the whole hierarchy and encapsulates its…

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…

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

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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