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Linearisable systems and the Gambier approach

S. Lafortune·B. Grammaticos·A. Ramani
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Abstract

A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the coupling of a Riccati equation with second order Painlevé equations. This is done in both continuous and discrete cases.

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S. Lafortune, B. Grammaticos, A. Ramani. 2001-04-06. Linearisable systems and the Gambier approach. https://arxiv.org/abs/nlin/0104018

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