The Gambier Mapping, Revisited
solv-int
2015-06-26 v1 Exactly Solvable and Integrable Systems
Abstract
We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable through linearisation. We then introduce the general discrete form of this equation, the Gambier mapping, and present conditions for its integrability. Finally, we obtain the reductions of the Gambier mapping, identify their integrable forms and compute their continuous limits.
Cite
@article{arxiv.solv-int/9804011,
title = {The Gambier Mapping, Revisited},
author = {B. Grammaticos and A. Ramani and S. Lafortune},
journal= {arXiv preprint arXiv:solv-int/9804011},
year = {2015}
}
Comments
11 pages, no figures, to be published in Physica A