S Lafortune et al 1998 Inverse Problems 14 287 doi:10.1088/0266-5611/14/2/005
S Lafortune
, B Grammaticos
and A Ramani§
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).
34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
Issue 2 (April 1998)
Received 13 May 1997
S Lafortune et al 1998 Inverse Problems 14 287
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