Jacek Szmigielski

On isospectral deformations of classical inhomogeneous strings

This talk is about 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 but are of independent interest. I will discuss how these new isospectral deformations result in evolution equations on the mass density whose form depends on how the string is tied at the endpoints. Also, if time permits, I will discuss why the evolution equations in this class linearize on the spectral side and hence can be solved by the inverse spectral method. As an example, I will discuss the problem involving a mass density given by a discrete finite measure and arbitrary boundary conditions which, as it turns out, can be solved by Stieltjes' continued fractions.

This is joint work with D. Gomez (University of British Columbia, Canada) and K. Colville (McGill University, Montreal, Canada).

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