  In this paper we consider a class of isospectral deformations of the
inhomogeneous string boundary value problem. The deformations considered are
generalizations of the isospectral deformation that has arisen in connection
with the Camassa-Holm equation for the shallow water waves. It is proved that
these new isospectral deformations result in evolution equations on the mass
density whose form depends on how the string is tied at the endpoints.
Moreover, it is shown that the evolution equations in this class linearize on
the spectral side and hence can be solved by the inverse spectral method. In
particular, the problem involving a mass density given by a discrete finite
measure and arbitrary boundary conditions is shown to be solvable by Stieltjes'
continued fractions.
