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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/340715 |
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| Summary: | 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. |
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| ISSN: | 1687-9643 1687-9651 |