No abstract

dedicated to gian-carlo rotaClassical results of Stieltjes are used to obtain explicit formulas for the peakon antipeakon solutions of the Camassa Holm equation. The closed form solution is expressed in terms of the orthogonal polynomials of the related classical moment problem. It is shown that collisions occur only in peakon antipeakon pairs, and the details of the collisions are analyzed using results from the moment problem. A sharp result on the steepening of the slope at the time of collision is given. Asymptotic formulas are given, and the scattering shifts are calculated explicitly. Academic Press

No abstract

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.