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We show that the super-Lax operator for $~N=1$~ supersymmetricKadomtsev-Petviashvili equation of Manin and Radul in three-dimensions can beembedded into recently developed self-dual supersymmetric Yang-Mills theory in$~2+2\-$dimensions, based on general features of its underlying super-Laxequation. The differential geometrical relationship in superspace between theembedding principle of the super-Lax operator and its associated super-Satoequation is clarified. This result provides a good guiding principle for theembedding of other integrable sub-systems in the super-Lax equation into thefour-dimensional self-dual supersymmetric Yang-Mills theory, which is theconsistent background for $~N=2$~ superstring theory, and potentially generatesother unknown supersymmetric integrable models in lower-dimensions.Comment: LATEX (with all macros), 11 pages, UMDEPP 94-47 (October 1993

SUPER-LAX OPERATOR EMBEDDED IN SELF-DUAL SUPERSYMMETRIC YANG-MILLS THEORY