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

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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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     author = {T. A. Ivanova and A. D. Popov},
     title = {Self-dual {Yang--Mills} fields in $d=4$ and integrable systems in~$1\leq d\leq 3$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {102},
     number = {3},
     year = {1995},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_3_a7/}
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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/