Discrete Painleve II equation over finite fields

Abstract

We investigate the discrete Painleve II equation over finite fields. We treat it over local fields and observe that it has a property that is similar to the good reduction over finite fields. We can use this property, which seems to be an arithmetic analogue of singularity confinement, to avoid the indeterminacy of the equations over finite fields and to obtain special solutions from those defined originally over fields of characteristic zero.

9 pages

References in corpus (3)

• Rational Solutions for the Discrete Painlevé II Equation
• The Hirota equation over finite fields. Algebro-geometric approach and multisoliton solutions
• Discrete Integrable Equations over Finite Fields

Cited by in corpus (8)

• Some integrable maps and their Hirota bilinear forms
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• Singularities of the discrete KdV equation and the Laurent property
• Multi-indexed Wilson and Askey-Wilson Polynomials
• Integrability of Discrete Equations Modulo a Prime
• The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields
• Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields