  We show that the super-Lax operator for $~N=1$~ supersymmetric
Kadomtsev-Petviashvili equation of Manin and Radul in three-dimensions can be
embedded into recently developed self-dual supersymmetric Yang-Mills theory in
$~2+2\-$dimensions, based on general features of its underlying super-Lax
equation. The differential geometrical relationship in superspace between the
embedding principle of the super-Lax operator and its associated super-Sato
equation is clarified. This result provides a good guiding principle for the
embedding of other integrable sub-systems in the super-Lax equation into the
four-dimensional self-dual supersymmetric Yang-Mills theory, which is the
consistent background for $~N=2$~ superstring theory, and potentially generates
other unknown supersymmetric integrable models in lower-dimensions.

High Energy Physics - Theory