4 research outputs found
Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy
The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou,
Capel and Quispel in 1992 as the family of partial difference equations
generalizing to higher rank the lattice Korteweg-de Vries systems, and includes
in particular the lattice Boussinesq system. We present a Lagrangian for the
generic member of the lattice Gel'fand-Dikii hierarchy, and show that it can be
considered as a Lagrangian 2-form when embedded in a higher dimensional
lattice, obeying a closure relation. Thus the multiform structure proposed in
arXiv:0903.4086v2 [nlin.SI] is extended to a multi-component system.Comment: 12 page