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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am31-3-8,
author = {A. Lesfari and A. Elachab},
title = {On the integrability of the generalized Yang-Mills system},
journal = {Applicationes Mathematicae},
volume = {31},
year = {2004},
pages = {345-351},
zbl = {1125.37050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-3-8}
}
A. Lesfari; A. Elachab. On the integrability of the generalized Yang-Mills system. Applicationes Mathematicae, Tome 31 (2004) pp. 345-351. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-3-8/