Second-degree Painlevé Equations and Their Contiguity Relations

    2014, Volume 19, Number 1, pp.  37-47

    Author(s): Grammaticos B., Ramani A., Guha P.

    We study second-order, second-degree systems related to the Painlevé equations which possess one and two parameters. In every case we show that by introducing a quantity related to the canonical Hamiltonian variables it is possible to derive such a second-degree equation. We investigate also the contiguity relations of the solutions of these higher-degree equations. In most cases these relations have the form of correspondences, which would make them non-integrable in general. However, as we show, in our case these contiguity relations are indeed integrable mappings, with a single ambiguity in their evolution (due to the sign of a square root).
    Keywords: Painlevé equations, contiguity relations, second-degree differential equations, Hamiltonian formalism
    Citation: Grammaticos B., Ramani A., Guha P., Second-degree PainlevĂ© Equations and Their Contiguity Relations, Regular and Chaotic Dynamics, 2014, Volume 19, Number 1, pp. 37-47

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