Linearization And Solutions Of The Discrete Painlevé-III Equation
B. Grammaticos, F. W. Nijhoff, V. Papageorgiou, A. Ramani
Abstract
We present particular solutions of the discrete Painlevé III (d-PIII) 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-PIII and confirm its integrability by explicitly deriving its Lax pair.
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