On the Inverse Spectral Problem for the Camassa-Holm Equation

Abstract

A key basis for seeking periodic solutions of the Camassa-Holm equation is to understand the associated spectral problemy′=14y+λmy.The periodic spectrum can be recovered from the norming constants and the elements of the auxiliary spectrum. The potential can then be reconstructed from the periodic spectrum. A necessary and sufficient condition for exponential decrease of the widthsλ2n-λ2n-1for a sequence 0 m∈C1(R). © 1998 Academic Press.