arXiv subjects

F. V. Andreev

Publications and source records attributed to F. V. Andreev.

3 recordsLinked to original sources

arXiv2019

Connection Formulae for Asymptotics of the Fifth Painlevé Transcendent on the Imaginary Axis: I

Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlevé equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \frac{d}{dλ}Y= \left(\frac t2σ_3 + \frac{A_0}λ+\frac{A_1}{λ-1}\right)Y. $$ The parametrization allows one to derive connection formulas for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulas are also considered.

math.CA↗

arXiv2001

Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and Algebraic Solutions of the Sixth Painlevé Equation

Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations ($RS$-transformations) are used to construct algebraic solutions of the sixth Painlevé equation. $RS$-Transformations of the ranks 3 and 4 of $2\times2$ matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.

nlin.SI↗

arXiv2001

Some Examples of RS^2_3(3)-Transformations of Ranks 5 and 6 as the Higher Order Transformations for the Hypergeometric Function

A combination of rational mappings and Schlesinger transformations for a matrix form of the hypergeometric equation is used to construct higher order transformations for the Gauss hypergeometric function.

nlin.SI↗