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

TL;DR

This paper derives the Davey-Stewartson equations from a zero curvature condition linked to SL(2,R) and demonstrates their connection to self-duality conditions in higher dimensions, providing a geometric perspective on these integrable systems.

Contribution

It establishes a novel derivation of Davey-Stewartson equations from higher-dimensional self-duality conditions using zero curvature formulations.

Findings

Derivation of Davey-Stewartson equations from zero curvature conditions.

Connection between 2+1 dimensional equations and 3+3 dimensional self-duality.

Insight into geometric origins of integrable equations.

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.