arXiv subjects

Shoji Okumura

Publications and source records attributed to Shoji Okumura.

5 recordsLinked to original sources

arXiv2006

Special Solutions of the Sixth Painleve Equation with Solvable Monodromy

We will study two types of special solutions of the sixth Painleve equation, which are invariant under the symmetries obtained from the Backlund transformations. In most cases, the fixed points of the Backlund transformations are classical solution, but our solutions are not classical for generic parameters. We will calculate the linear monodromy of these solutions exactly, and we will characterize them on Fricke's cubic surface of monodromy.

math.CA↗

arXiv2006

Complete coalescent diagram of the Painleve equations

We will revise Garnier-Okamoto's coalescent diagram of isomonodromic deformations and give a complete coalescent diagram. In our viewpoint, we have ten types of isomonodromic deformations and two of them give the same type of the Painlevé equation. We can naturally put the thirty-fourth Painleve equation in our diagram, which corresponds to the Flaschka-Newell form of the second Painlevé equation.

math.CA↗

arXiv2005

R. Fuchs' problem of the Painleve equations from the first to the fifth

We will classify all rational transformations which change the confluent hypergeometric equations to linear equations of the Painleve type from the first to the fifth. We show such rational transformations correspond to almost all of algebraic solutions of the Painleve equations from the first to fifth up to the Backlund transformations.

math.CA↗

arXiv2002

The Indefinite Self-Dual Metrics and Painleve Equations

We classify the SU(2)-invariant anti-self-dual metrics with a signature (+,+,-,-). The metrics are specified by a solution of Painleve VI, V, III or II. Moreover we show the geometric meaning of the metrics specified by each type of Painlevé functions.

math-ph↗

arXiv2000

The Scalar-flat Kaehler Metric and Painleve III

We study the anti-self-dual equation for non-diagonal SU(2)-invariant metrics and give an equivalent ninth-order system. This system reduce to a sixth-order system if the metric is in the conformal class of scalar-flat-Kaehler metric.

math-ph↗