Linearisable systems and the Gambier approach

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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8 pages, no figure

Scientific paper

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 Painlev\'e
equations. This is done in both continuous and discrete cases.

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