arXiv subjects

Anastasia Parusnikova

Publications and source records attributed to Anastasia Parusnikova.

4 recordsLinked to original sources

arXiv2025

On finding formal power-logarithmic expansions of solutions to $q$-difference equations

An algebraic $q$-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain $q$-difference analogue of the fifth Painlevé equation for specific values of the equation parameters is given; two different values of the number $q$ are considered, leading to qualitatively different formal asymptotic expansions of the solutions of the fifth Painlevé equation.

math.CA↗

arXiv2017

On Divergence of Puiseux Series Asymptotic Expansions of Solutions to the Third Painlevé Equation

In this paper we present a family of values of the parameters of the third Painlevé equation such that Puiseux series formally satisfying this equation -- considered as series of $z^{2/3}$ -- are series of exact Gevrey order one. We prove the divergence of these series and provide analytic functions which are approximated by them in sectors with the vertices at infinity.

math.CA↗

arXiv2014

4-Dimensional Power Geometry and its Application to $P_1$ -- $P_5$

In the first section of this work we introduce 4-dimensional Power Geometry for second-order ODEs of a polynomial form. In the next five sections we apply this construction to the first five Painlevé equations.

math.CA↗

arXiv2013

On Gevrey orders of power expansions of solutions to the third and fifth Painlevé equations

The question under consideration is Gevrey summability of power expansions of solutions to the third and fifth Painlevé equations near infinity. Methods of French and Japaneese schools are used to analyse these properties of formal power-series solutions. The results obtained are compared with the ones obtained by means of Power Geometry.

math.CA↗