Discrete systems related to some equations of the Painlevé-Gambier classification

Details Discrete systems related to some equations of the Painlevé-Gambier classification Discrete systems related to some equations of the Painlevé-Gambier classification

2001-04-06

arxiv.org/abs/nlin/0104019v1

Physics Letters A 270, 55-61 (2000)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

10.1016/S0375-9601(00)00259-0

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six transcendental Painlev\'e equations were obtained. In the case of the Gambier equation we give the contiguity relations for both the continuous and the discrete system.

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