  A pluri-Lagrangian structure is an attribute of integrability for lattice
equations and for hierarchies of differential equations. It combines the notion
of multi-dimensional consistency (in the discrete case) or commutativity of the
flows (in the continuous case) with a variational principle. Recently we
developed a continuum limit procedure for pluri-Lagrangian systems, which we
now apply to most of the ABS list and some members of the lattice
Gelfand-Dickey hierarchy. We obtain pluri-Lagrangian structures for many
hierarchies of integrable PDEs for which such structures where previously
unknown. This includes the Krichever-Novikov hierarchy, the double hierarchy of
sine-Gordon and modified KdV equations, and a first example of a continuous
multi-component pluri-Lagrangian system.
