The degenerate third Painlev\'{e} equation, $u^{\prime \prime} =
\frac{(u^{\prime})^{2}}{u} - \frac{u^{\prime}}{\tau} + \frac{1}{\tau}(-8
\epsilon u^{2} + 2ab) + \frac{b^{2}}{u}$, where $\epsilon,b \in \mathbb{R}$,
and $a \in \mathbb{C}$, and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as $\tau \to \pm 0$ and $\pm i0$ solution and general regular as $\tau
\to \pm \infty$ and $\pm i \infty$ solution are obtained.
Publié le : 2003-12-03
Classification:
Mathematics - Classical Analysis and ODEs,
Mathematical Physics,
Nonlinear Sciences - Exactly Solvable and Integrable Systems,
33E17, 34M40, 34M50, 34M55, 34M60
@article{0312075,
author = {Kitaev, A. V. and Vartanian, A. H.},
title = {Connection Formulae for Asymptotics of Solutions of the Degenerate Third
Painlev\'{e} Equation. I},
journal = {arXiv},
volume = {2003},
number = {0},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/0312075}
}
Kitaev, A. V.; Vartanian, A. H. Connection Formulae for Asymptotics of Solutions of the Degenerate Third
Painlev\'{e} Equation. I. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312075/