Multipeakons and the Classical Moment Problem

Details Multipeakons and the Classical Moment Problem Multipeakons and the Classical Moment Problem

1999-06-04

arxiv.org/abs/solv-int/9906001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

32 pages, 3 figures; to appear in Advances in Mathematics

Scientific paper

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

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