Multipeakons and the Classical Moment Problem
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
Classical 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
Cite
@article{arxiv.solv-int/9906001,
title = {Multipeakons and the Classical Moment Problem},
author = {Richard Beals and D. H. Sattinger and J. Szmigielski},
journal= {arXiv preprint arXiv:solv-int/9906001},
year = {2007}
}
Comments
32 pages, 3 figures; to appear in Advances in Mathematics