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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 102, Number 3, Pages 384–419
(Mi tmf1276)
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This article is cited in 22 scientific papers (total in 22 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf1276 https://www.mathnet.ru/eng/tmf/v102/i3/p384
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