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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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Received: 26.06.1994

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
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\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
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\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}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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