Isospectral deformations for Sturm-Liouville and Diractype operators and associated nonlinear evolution equations, Rep

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 study the Harry Dym equation in some detail and relate its solutions to KdV-solutions and to Hirota’s τ-functions. 1