The Gambier Mapping, Revisited

Details The Gambier Mapping, Revisited The Gambier Mapping, Revisited

1998-04-10

arxiv.org/abs/solv-int/9804011v1

Physica A 253, 260-270 (1998)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, no figures, to be published in Physica A

Scientific paper

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.

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