title: The string density problem and the Camassa-Holm equation.
abstract: Recently, the string density problem, considered in the pioneering work of M. G. Kreĭn, has arisen naturally in connection with the Camassa-Holm equation for shallow water waves. In this paper we review the forward and inverse string density problems, with some numerical examples, and relate it to the Camassa-Holm equation, with special reference to multi-peakon/anti-peakon solutions. Under stronger assumptions, the Camassa-Holm spectral problem and the string density problem can be transformed to the Schrödinger spectral problem and its inverse problem. Recent results exploiting this transformation are reviewed briefly.
authors.affiliation: Department of Mathematics, Yale University, New Haven, CT 06520-8283, USA.
authors.forename: Richard
authors.initials: R
authors.lastname: Beals
authors.forename: David H
authors.initials: DH
authors.lastname: Sattinger
authors.forename: Jacek
authors.initials: J
authors.lastname: Szmigielski