Constructing Integrable Third Order Systems:The Gambier Approach

Details Constructing Integrable Third Order Systems:The Gambier Approach Constructing Integrable Third Order Systems:The Gambier Approach

1997-05-12

arxiv.org/abs/solv-int/9705007v1

Inverse Problems 14, 287-298 (1998)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, TEX FILE

Scientific paper

10.1088/0266-5611/14/2/005

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 the 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 Painlev\'e method for ODE's and the singularity confinement method for mappings).

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