On the Inverse Spectral Problem for the Camassa-Holm Equation

Author: Constantin A.  

Publisher: Academic Press

ISSN: 0022-1236

Source: Journal of Functional Analysis, Vol.155, Iss.2, 1998-06, pp. : 352-363

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Abstract

A key basis for seeking periodic solutions of the Camassa-Holm equation is to understand the associated spectral problemy'=y+lambdamy.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 widths lambda2n-lambda2n-1for a sequence 0mC1(R). Copyright 1998 Academic Press.