64 citations · 339 across the 27 of their papers we have counts for
27 papers
Painlevé Property and Generating Functions for Asymptotics
A. V. Kitaev
This paper proposes a new approach to the asymptotic analysis of Painlevé equations. The approach is based on representing solutions of the Painlevé equations using formal series i…
The Degenerate Third Painleve' Equation: Complete Asymptotic Classification of Solutions in the Neighbourhood of the Regular Singular Point
A. V. Kitaev, A. Vartanian
We give a classification for the small- asymptotic behaviours of solutions to the degenerate third Painlevé equation, $u^{''}(τ) = \frac{(u^{\prime}(τ))^{2}}{u(τ)} - \frac{u^{\p…
One-Parameter Meromorphic Solution of the Degenerate Third Painlevé Equation with Formal Monodromy Parameter Vanishing at the Origin
A. V. Kitaev, A. Vartanian
We prove that there exists a one-parameter meromorphic solution vanishing at of the degenerate third Painlevé equation, \begin{equation*} u^{\prime \prime}(τ) \! = \!…
Algebroid Solutions of the Degenerate Third Painlevé Equation for Vanishing Formal Monodromy Parameter
A. V. Kitaev, A. Vartanian
Various properties of algebroid solutions of the degenerate third Painlevé equation, \begin{equation*} u^{\prime \prime}(τ) \! = \! \frac{(u^{\prime}(τ))^{2}}{u(τ)} \! - \! \frac{u…
Connection Formulae for Asymptotics of the Fifth Painlevé Transcendent on the Imaginary Axis: I
F. V. Andreev, A. V. Kitaev
Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlevé equation as are found. These asymptotics are parameterized by mono…
Asymptotics of Integrals of Some Functions Related to the Degenerate Third Painlevé Equation
A. V. Kitaev, A. Vartanian
It is shown how to calculate asymptotics of integrals over the positive semi-axis of two functions related to the Degenerate Third Painlevé Equation (dP3). As an example, the corre…