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 .
Citation
Alexander D. Bruno. "Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations." Int. J. Differ. Equ. 2015 1 - 13, 2015. https://doi.org/10.1155/2015/340715
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