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

Abstract

The degenerate third Painlevé 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.

40 pages, LaTeX2e

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