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 TMF, 1995, Volume 102, Number 3, Pages 384–419 (Mi tmf1276)

Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$

T. A. Ivanova, A. D. Popov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: 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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English version:
Theoretical and Mathematical Physics, 1995, 102:3, 280–304

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Citation: T. A. Ivanova, A. D. Popov, “Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$”, TMF, 102:3 (1995), 384–419; Theoret. and Math. Phys., 102:3 (1995), 280–304

Citation in format AMSBIB
\Bibitem{IvaPop95} \by T.~A.~Ivanova, A.~D.~Popov \paper Self-dual Yang--Mills fields in $d=4$ and integrable systems in~$1\leq d\leq 3$ \jour TMF \yr 1995 \vol 102 \issue 3 \pages 384--419 \mathnet{http://mi.mathnet.ru/tmf1276} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1348851} \zmath{https://zbmath.org/?q=an:0854.58046} \transl \jour Theoret. and Math. Phys. \yr 1995 \vol 102 \issue 3 \pages 280--304 \crossref{https://doi.org/10.1007/BF01017880} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ02000008}