Belinskii-Zakharov Formulation for Bianchi models and Painleve III Equation
classification
🧮 math-ph
gr-qcmath.MP
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equationbianchimodelspainlevebelinskii-zakharovformulationarisesbecomes
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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.
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