Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy
Exactly Solvable and Integrable Systems
2015-05-14 v1
Abstract
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.
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Cite
@article{arxiv.0911.1234,
title = {Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy},
author = {S. B. Lobb and F. W. Nijhoff},
journal= {arXiv preprint arXiv:0911.1234},
year = {2015}
}
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12 pages