Classical limit of the Korteweg-de Vries hierarchy of isospectral transformations

The Korteweg-de Vries hierarchy of equations, whose solutions are quantum-mechanical isospectral potentials, is shown to reduce, in the classical limit, to a family of equations whose solutions are isoperiodic potentials. The quantum-mechanical spectra of several families of classically isoperiodic potentials are examined in the light of the above correspondence.