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Linearization And Solutions Of The Discrete Painlevé-III Equation

B. Grammaticos·F. W. Nijhoff·V. Papageorgiou·A. Ramani
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Abstract

We present particular solutions of the discrete Painlevé 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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B. Grammaticos, F. W. Nijhoff, V. Papageorgiou, A. Ramani. 1993-11-03. Linearization And Solutions Of The Discrete Painlevé-III Equation. https://doi.org/10.1016/0375-9601(94)91124-x

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