Linearization And Solutions Of The Discrete Painlevé-III Equation

Details Linearization And Solutions Of The Discrete Painlevé-III Equation Linearization And Solutions Of The Discrete Painlevé-III Equation

1993-11-03

arxiv.org/abs/solv-int/9310003v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1016/0375-9601(94)91124-X

We present particular solutions of the discrete Painlev\'e III (d-P$\rm_{III}$) equation of rational and special function (Bessel) type. These solutions allow us to establish a close parallel between this discrete equation and its continuous counterpart. Moreover, we propose an alternate form for d-P$\rm_{III}$ and confirm its integrability by explicitly deriving its Lax pair.

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