21 citations · 32 across the 3 of their papers we have counts for
5 papers
Semi-discrete Lagrangian 2-forms and the Toda hierarchy
Duncan Sleigh, Mats Vermeeren
We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lag…
Lagrangian multiforms on Lie groups and non-commuting flows
Vincent Caudrelier, Frank Nijhoff, Duncan Sleigh +1
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 ye…
Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy
Duncan Sleigh, Frank Nijhoff, Vincent Caudrelier
We present, for the first time, a Lagrangian multiform for the complete Kadomtsev-Petviashvili (KP) hierarchy -- a single variational object that generates the whole hierarchy and…
Variational symmetries and Lagrangian multiforms
D. G. Sleigh, F. W. Nijhoff, V. Caudrelier
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 Lag…
A Variational Approach to Lax Representations
D. G. Sleigh, F. W. Nijhoff, V. Caudrelier
It is shown that the Zakharov-Mihailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform struc…