Isospectral deformations for Strum-Liouville and Dirac-type operators and associated nonlinear evolution equations

Abstract We give a systematic account of isospectral deformations for Sturm-Liouville and Dirac-type operators and associated hierarchies of nonlinear evolution equations. In particular, we study generalized KdV and modified KdV-hierarchies and their reduction to the standard (m)KdV- hierarchy. As an example we discuss the Harry Dym equation in some detail and relate its solutions to KdV-solutions and to Hirota's τ-functions.

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