The Gambier mapping, revisited

B. Grammaticos, A. Ramani and S. Lafortune

Physica A: Statistical Mechanics and its Applications, 1998, vol. 253, issue 1, 260-270

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.

Keywords: Integrability; Linearizability; Discrete systems (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:253:y:1998:i:1:p:260-270

DOI: 10.1016/S0378-4371(97)00675-4

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