Integrability criterion in terms of coprime property for the discrete Toda equation

Abstract

We reformulate the singularity confinement of the discrete Toda equation. We prove the co-primeness property, which has been introduced in our previous paper (arXiv:1311.0060) as one of the integrability criteria, for the discrete Toda equation. We study three types of boundary conditions (semi-infinite, molecule, periodic) for the discrete Toda equation, and prove that the same co-primeness property holds for all the types of boundaries. (v2: typos corrected, final version to appear in J. Math. Phys.)

arXiv comment31 pages, 4 figures

References in corpus (5)

• Algebraic entropy
• Singularity confinement and chaos in discrete systems
• Discrete Painleve II equation over finite fields
• Irreducibility and co-primeness as an integrability criterion for discrete equations
• Singularities of the discrete KdV equation and the Laurent property

Cited by in corpus (6)

• Singularity confinement and chaos in two-dimensional discrete systems
• Algebraic entropy of an extended Hietarinta-Viallet equation
• Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation
• Degree growth of lattice equations defined on a 3x3 stencil
• Nonlinear forms of coprimeness preserving extensions to the Somos-$4$ recurrence and the two-dimensional Toda lattice equation --investigation into their extended Laurent properties--
• Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice