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 …

A variational structure for the potential AKP system is established using the novel formalism
of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on …

A Lagrangian multiform structure is established for a generalisation of the Darboux system
describing orthogonal curvilinear coordinate systems. It has been shown in the past that this …

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 …

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 …

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 …

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 …

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 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 …