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First integrals of a generalized Darboux-Halphen system.
preprint
posted on 2005-08-24, 13:49 authored by S. Chakravarty, R.G. HalburdA 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.
History
School
- Science
Department
- Mathematical Sciences
Pages
387096 bytesPublication date
2002Notes
This pre-print has been submitted, and accepted, to the journal, Journal of Mathematical Physics [© American Institute of Physics]. The definitive version: HALBURD, R. and CHAKRAVARTY, S., 2003. First integrals of a generalized Darboux-Halphen system. Journal of Mathematical Physics, 44(4), pp. 1751-1762, is available at: http://jmp.aip.org/jmp/.Language
- en