Multipeakons and the Classical Moment Problem

Multipeakons and the Classical Moment Problem

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...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2000-09, Vol.154 (2), p.229-257
Hauptverfasser: Beals, Richard, Sattinger, David H., Szmigielski, Jacek
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Sprache:eng
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collisions
continued fractions
multipeakons
scattering
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container_title Advances in mathematics (New York. 1965)
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creator Beals, Richard
Sattinger, David H.
Szmigielski, Jacek
description 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.
doi_str_mv 10.1006/aima.1999.1883
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subjects collisions
continued fractions
multipeakons
scattering
title Multipeakons and the Classical Moment Problem
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