Geodesic
Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 384-419 
T. A. Ivanova; A. D. Popov. Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 384-419. http://geodesic.mathdoc.fr/item/TMF_1995_102_3_a7/
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     author = {T. A. Ivanova and A. D. Popov},
     title = {Self-dual {Yang{\textendash}Mills} fields in $d=4$ and integrable systems in~$1\leq d\leq 3$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Ward correspondence between self-dual Yang–Mills fields and holomorphic vector bundles is used to develop a method for reducing the Lax pair for the self-duality equations of the Yang–Mills model in $d=4$ with respect to the action of continuous symmetry groups. It is well known that reductions of the self-duality equations lead to systems of nonlinear differential equations in dimension $1\leq d\leq 3$. For the integration of the reduced equations, it is necessary to find a Lax pair whose compatibility conditions is these equations. The method makes it possible to obtain systematically a Lax representation for the reduced self-duality equations. This is illustrated by a large number of examples.

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