Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations

Alexander D. Bruno

International Journal of Differential Equations, 2015, vol. 2015, 1-13

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 .

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:340715

DOI: 10.1155/2015/340715

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