Lagrangian multiforms provide a variational framework to describe integrable hierarchies.
The case of Lagrangian 1-forms covers finite-dimensional integrable systems. We use the …

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 …

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 …

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 …

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

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 …

Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of
integrability, and by the results of the authors on the role of covariant Hamiltonian formalism …

We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by
formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and …

Generalised Hydrodynamics (GHD) describes the large-scale inhomogeneous dynamics of
integrable (or close to integrable) systems in one dimension of space, based on a central …

A new notion of integrability called the multi-dimensional consistency for the integrable
systems with the Lagrangian 1-form structure is captured in the geometrical language for …