Rational Solutions for the Discrete Painlevé II Equation

Abstract

The rational solutions for the discrete Painlevé II equation are constructed based on the bilinear formalism. It is shown that they are expressed by the determinant whose entries are given by the Laguerre polynomials. Continuous limit to the Devisme polynomial representation of the rational solutions for the Painlevé II equation is also discussed.

12 pages, latex

References in corpus (2)

• Determinant Structure of the Rational Solutions for the Painlevé II Equation
• Cellular Automata and Ultra-Discrete Painlevé Equations

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• Discrete Painleve II equation over finite fields
• Random ballistic growth and diffusion in symmetric spaces
• On Rational Solutions of Dressing Chains of Even Periodicity
• Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation
• Hypergeometric solutions to ultradiscrete Painleve equations
• Discrete equations from Bäcklund transformations of the fifth Painlevé equation