First integrals of a generalized Darboux-Halphen system.

A third-order system of nonlinear, ordinary differential equations depending on 3 arbitrary parameters is analyzed. The system arises in the study of SU(2)-invariant hypercomplex manifolds and is a dimensional reduction of the self-dual Yang-Mills equation. The general solution, first integrals and...

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Bibliographic Details
Main Authors: S. Chakravarty, R.G. Halburd
Format: Default Preprint
Published: 2002
Subjects:
Other mathematical sciences not elsewhere classified
Darboux-Halphen
mathematics
equations
Mathematical Sciences not elsewhere classified
Online Access:https://hdl.handle.net/2134/443
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Summary:A third-order system of nonlinear, ordinary differential equations depending on 3 arbitrary parameters is analyzed. The system arises in the study of SU(2)-invariant hypercomplex manifolds and is a dimensional reduction of the self-dual Yang-Mills equation. The general solution, first integrals and the Nambu-Poisson structure of the system are explicitly derived. It is shown that the first integrals are multi-valued on the phase space even though the general solution of the system is single-valued for special choices of parameters.

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