Abstract:
A rather general ordinary differential equation is considered that can be represented as a polynomial in variables and derivatives. For this equation, the concept of power-elliptic expansions of its solutions is introduced and a method for computing them is described. It is shown that such expansions of solutions exist for the first and second Painlevé equations.
Key words:ordinary differential equation, asymptotic expansion of solutions, elliptic asymptotic behavior, first and second Painlevé equations.
Fulltext:
PDF file (286 kB)