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-SDYM Fields and Heavenly Spaces. I. -SDYM equations as an integrable system

arXiv:math-ph/0412011 · doi:10.1088/0305-4470/38/20/008

Abstract

It is shown that the self-dual Yang-Mills (SDYM) equations for the -bracket Lie algebra on a heavenly space can be reduced to one equation (the \it master equation\rm). Two hierarchies of conservation laws for this equation are constructed. Then the twistor transform and a solution to the Riemann-Hilbert problem are given.

25 pages

$\ast$-SDYM Fields and Heavenly Spaces. I. $\ast$-SDYM equations as an integrable system · wovepaper