International Journal of Differential Equations

Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations

Alexander D. Bruno

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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 P1,,P6.

Article information

Source
Int. J. Differ. Equ., Volume 2015 (2015), Article ID 340715, 13 pages.

Dates
Received: 30 January 2014
Accepted: 24 June 2014
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881428

Digital Object Identifier
doi:10.1155/2015/340715

Mathematical Reviews number (MathSciNet)
MR3312759

Zentralblatt MATH identifier
1339.34063

Citation

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


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References

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