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Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations

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  • Alexander D. Bruno

Abstract

We consider an ordinary differential equation (ODE) which can be written as a polynomial in variables and derivatives. Several types of asymptotic expansions of its solutions can be found by algorithms of 2D Power Geometry. They are power, power-logarithmic, exotic, and complicated expansions. Here we develop 3D Power Geometry and apply it for calculation power-elliptic expansions of solutions to an ODE. Among them we select regular power-elliptic expansions and give a survey of all such expansions in solutions of the Painlevé equations .

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  • Alexander D. Bruno, 2015. "Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations," International Journal of Differential Equations, Hindawi, vol. 2015, pages 1-13, February.
    • Handle: RePEc:hin:jnijde:340715
    DOI: 10.1155/2015/340715
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