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KIAM Preprint  88, Moscow, 2013
Authors: Bruno A. D.
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 P1,,P6.
Power Geometry, asymptotic expansion, Painleve equations
Publication language: english,  pages: 28
Research direction:
Mathematical modelling in actual problems of science and technics
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About authors:
  • Bruno Alexander Dmitrievich, RAS