## 13 Citations

### Variational symmetries and Lagrangian multiforms

- MathematicsLetters 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

- 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…

### 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…

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

- Computer ScienceLetters 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

- MathematicsJournal of Geometry and Physics
- 2023

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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

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

- MathematicsJournal of Geometry and Physics
- 2020

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

- MathematicsInternational Mathematics Research Notices
- 2021

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

- MathematicsEuropean Journal of Mathematics
- 2020

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

- 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…

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