THE ORIGIN OF GAUGE SYMMETRIES IN INTEGRABLE SYSTEMS OF THE KdV TYPE

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Abstract
Generalized systems of integrable nonlinear differential equations of the KdV type are considered from the point of view of self-dual Yang-Mills theory in space-times with signature (2, 2). We present a systematic method for embedding the rth flows of the SL(N) KdV hierarchy with N≥2 and rN the corresponding equations can be described in a similar fashion, provided that (in general) the rank of the gauge group increases accordingly. Certain connections of this formalism with WN algebras are also discussed. Finally, we obtain a new class of nonlinear systems in two dimensions by introducing self-dual Ansätze associated with the algebras of Bershadsky and Polyakov.

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