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Constructing integrable third-order systems: the Gambier approach

S Lafortune-+, B Grammaticos++ and A Ramani§

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We present a systematic construction of integrable third-order systems based on the coupling of an integrable second-order equation and a Riccati equation. This approach is an extension of the Gambier method that led to the equation that bears his name. Our study is carried through for both continuous and discrete systems. In both cases the investigation is based on the study of the singularities of the system (the Painlevé method for ordinary differential equations and the singularity confinement method for mappings).


PACS

02.30.Ik Integrable systems

02.30.Hq Ordinary differential equations

MSC

34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)

Subjects

Mathematical physics

Dates

Issue 2 (April 1998)

Received 13 May 1997



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