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On the integrability of the generalized Yang-Mills system

A. LesfariA. Elachab — 2004

Applicationes Mathematicae

We consider a hamiltonian system which, in a special case and under the gauge group SU(2), can be considered as a reduction of the Yang-Mills field equations. We prove explicitly, using the Lax spectral curve technique and the van Moerbeke-Mumford method, that the flows generated by the constants of motion are straight lines on the Jacobi variety of a genus two Riemann surface.

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