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

Abstract

It is shown that the self-dual Yang-Mills (SDYM) equations for the $\ast$-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

References in corpus (6)

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Cited by in corpus (6)

• Twistor theory at fifty: from contour integrals to twistor strings
• New heavenly double copies
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms
• $\ast$-SDYM fields and heavenly spaces: II. Reductions of the $\ast$-SDYM system
• Self-dual gravity via Hitchin's equations
• On an integrable deformation of Kapustin-Witten systems