Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation. I

Details Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation. I Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation. I

2003-12-03

arxiv.org/abs/math/0312075v1

Mathematics

Classical Analysis and ODEs

40 pages, LaTeX2e

Scientific paper

10.1088/0266-5611/20/4/010

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.

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