SOME REDUCTIONS OF THE SELF-DUAL YANG-MILLS EQUATIONS TO INTEGRABLE SYSTEMS IN 2+1-DIMENSIONS

A reduction of the self-dual Yang-Mills (SDYM) equations is studied by imposing two space-time symmetries and by requiring that the connection one-form belongs to a Lie algebra of formal matrix-valued differential operators in an auxiliary variable. In this article, the scalar case and the canonical cases for 2X2 matrices are examined. In the scalar case, it is shown that the field equations can be reduced to the forced Burgers equation. In the matrix case, several well-known 2+1 integrable equations are obtained. Also examined are certain transformation properties between the solutions of some of these 2+1 equations. © 1995 American Institute of Physics.