Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0662.34056
Kitaev, A.V.
The method of isomonodromy deformations and asymptotics of solutions of the ``complete'' third Painlevé equation. (Russian)
[J] Mat. Sb., N. Ser. 134(176), No.3(11), 421-444 (1987).

Using the method of the monodromy preserving deformation, the author studies a $2\times2$ matrix linear ordinary differential equation $$ \Phi\sb\lambda = \tau \left\{-i\sigma\sb3 - \frac{ai}{2\tau\lambda} \sigma\sb3 - \frac1\lambda \pmatrix 0 & C \\ D & 0 \endpmatrix + \frac{i}{2\lambda\sp2} \pmatrix \sqrt{\theta\sp2-AB} & A \\ B & -\sqrt{\theta\sp2-AB} \endpmatrix \right\} \Phi, \tag1 $$ where $\sigma\sb3 = \pmatrix 1 & 0 \\ 0 & -1 \endpmatrix$, $\theta\sp2=1$ and $A = A(\tau)$, $B = B(\tau)$, $C = C(\tau)$, $D = D(\tau)$ are meromorphic functions in the region $\Re\tau>0$. He obtains asymptotic formulas for the solutions of the ``complete'' third Painlevé equation $$ u\sb{zz} = \frac{u\sp2\sb z}{u} - \frac{u\sb z}{z} + \frac{1}{z} (\hat au\sp2 u\sp2 + \hat b) + \hat c u\sp3 + \frac{\hat d}{u}, \quad \hat c\hat d\ne 0, $$ the solutions of which are connected with the monodromy preserving deformations of the coefficients of (1).
[J.Kalas]

MSC 2000:: *34E05 Asymptotic expansions (ODE)

Keywords: monodromy preserving deformation; third Painlevé equation

Cited in: Zbl 0716.34073

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]