$\ast$-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.