THE SCATTERING APPROACH FOR AN INTEGRABLE SHALLOW WATER EQUATION

JONATAN LENELLS

jonatan@maths.lth.se

Department of Mathematics

Lund University

Box 118

SE-22100 Lund, Sweden

Lund University

Box 118

SE-22100 Lund, Sweden

The isospectral problem for the Camassa-Holm shallow
water equation is a weighted Sturm-Liouville problem. The spectral
data consists of a continuous spectrum and a finite or infinite number
of eigenvalues. We present an approach for determining the evolution
of the scattering data, applicable independently of the number of
eigenvalues. In the case of finitely many eigenvalues the initial
value problem can be solved by the inverse
scattering method.

EPSRC Gregynog Workshop, 21-26 July 2002