International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2015 (2015), Article ID 340715, 13 pages.
Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations
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 .
Int. J. Differ. Equ., Volume 2015 (2015), Article ID 340715, 13 pages.
Received: 30 January 2014
Accepted: 24 June 2014
First available in Project Euclid: 20 January 2017
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Bruno, Alexander D. Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations. Int. J. Differ. Equ. 2015 (2015), Article ID 340715, 13 pages. doi:10.1155/2015/340715. https://projecteuclid.org/euclid.ijde/1484881428