Power Geometry and elliptic expansions of solutions to the Painlevé equations

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 P_{1},…,P_{6}.

Keywords:

Power Geometry, asymptotic expansion, Painleve equations

Publication language:english, pages:28

Research direction:

Mathematical modelling in actual problems of science and technics