The Hunting for the Discrete Painleve Equations

    2000, Volume 5, Number 1, pp.  53-66

    Author(s): Grammaticos B., Ramani A.

    We review our findings on discrete Painleve equations with emphasis on the two direct methods we have proposed for their derivation: deautonomisation through singularity confinement and geometrical approach based on affine Weyl groups. The question of integrability of discrete Painleve equations is also addressed in terms of the existence of a Lax pair or of a description in the frame of the Grand Scheme. A list of discrete Painleve equations, as complete as possible but still not exhaustive, is also presented.
    Citation: Grammaticos B., Ramani A., The Hunting for the Discrete Painleve Equations, Regular and Chaotic Dynamics, 2000, Volume 5, Number 1, pp. 53-66

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