Asymptotic Expansions of Solutions to the Hierarchy of the Fourth Painlevé Equation
Аношин В. И., Бекетова А. Д., Parusnikova A.
M.: Max press, 2021
, Moscow Mathematical Journal 2015 Vol. 15 No. 4 P. 805-815
In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given k-isogeny class over a finite field k. © 2015 Independent University of Moscow. ...
Added: March 2, 2016
, Mathematical notes 2019 Vol. 105 No. 4 P. 592-603
The Riccati equation with coefficients expandable in convergent power series in a neigh- borhood of infinity are considered. Extendable solutions of such equations are studied. Methods of power geometry are used to obtain conditions for convergent series expansions of these solutions. An algorithm for deriving such series is given. ...
Added: April 10, 2019
, Mathematical notes 2021 Vol. 110 No. 1 P. 135-144
Scalar real Riccati equations with coefficients expanding in convergent power series in a neighborhood of infinity is considered. Continued solutions of such equations are studied. Power geometry methods are used to obtain conditions for expanding these solutions in asymptotic series. ...
Added: September 21, 2021
On Various Approaches to Asymptotics of Solutions to the Third Painlevé Equation in a Neighborhood of Infinity
, , Journal of Mathematical Sciences 2019 Vol. 241 No. 3 P. 318-326
We examine asymptotic expansions of the third Painlevé transcendents for αδ ≠ 0 and γ = 0 in the neighborhood of infinity in a sector of aperture <2π by the method of dominant balance). We compare intermediate results with results obtained by methods of three-dimensional power geometry. We find possible asymptotics in terms of elliptic ...
Added: October 26, 2019
On Gevrey orders of formal power series solutions to the third and fifth Painlevé equations near infinity
, Opuscula Mathematica 2014 Vol. 34 No. 3 P. 591-599
The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painlevй equations near infinity. We consider the fifth Painleve equation in two cases: when αβγδ \neq 0 and when αβγ \neq 0, δ = 0 and the third Painlevé equation when all the parameters of the equation are ...
Added: February 28, 2014
, Qualitative Theory of Dynamical Systems 2022 Vol. 21 Article 47
We consider a nonlinear ordinary differential equation of arbitrary order with coefficients in the form of power series that converge in a neighborhood of the origin. The methods created in power geometry in recent years make it possible to compute formal solutions to that equation in the form of Dulac series. We describe the corresponding algorithm and prove a sufficient ...
Added: April 10, 2022