Integrability, Monodromy Evolving Deformations, and Self-Dual Bianchi IX Systems

Details Integrability, Monodromy Evolving Deformations, and Self-Dual Bianchi IX Systems Integrability, Monodromy Evolving Deformations, and Self-Dual Bianchi IX Systems

Feb 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phrvl..76..857c&link_type=abstract

Physical Review Letters, Volume 76, Issue 6, February 5, 1996, pp.857-860

Mathematics

Logic

10

Scientific paper

We derive a nonlinear system of ODE's related to complex Bianchi IX metrics with self-dual Weyl curvature from the compatibility conditions of a novel type of monodromy evolving linear system. The analysis of the linear system yields a nontrivial separation of variables leading to the general solution of the nonlinear equations. In general, the solution is densely branched, but we find a single valued family of special solutions corresponding to the self-dual Bianchi IX, vacuum Einstein equations. These nonlinear equations also arise in fluid dynamics and in two-dimensional topological field theories.

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