Belinskii-Zakharov Formulation for Bianchi models and Painleve III Equation

Abstract

We show that \a < 0, \b > 0, \g=\d=0 Painleve III equation arises as a zero-curvature condition in the Belinskii-Zakharov inverse-scattering formulation for Bianchi cosmological models. For special values of the parameters this Painleve III equation becomes the dynamical equation for Bianchi I, II, VI_0 and VII_0 models.

12 pages

References in corpus (3)

• Canonical quantization of cylindrical gravitational waves with two polarizations
• Canonical Structure of Locally Homogeneous Systems on Compact Closed 3-Manifolds of Types $E^3$, Nil and Sol
• Painleve III Equation and Bianchi VII_0 Model

Cited by in corpus (2)

• Classical and Quantum Features of the Mixmaster Singularity
• The General Solution of Bianchi Type III Vacuum Cosmology