Davey-Stewartson Equation from a Zero Curvature and a Self-Duality Condition

Abstract

We derive the two equations of Davey-Stewartson type from a zero curvature condition associated with SL(2,{\bf R}) in $2+1$ dimensions. We show in general how a $2+1$ dimensional zero curvature condition can be obtained from the self-duality condition in $3+3$ dimensions and show in particular how the Davey-Stewartson equations can be obtained from the self-duality condition associated with SL(2,{\bf R}) in $3+3$ dimensions.