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Multi-peakons and a theorem of Stieltjes

R Beals-+, D H Sattinger++ and J Szmigielski§

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LETTER TO THE EDITOR

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.


PACS

02.10.Ud Linear algebra

02.30.Ik Integrable systems

02.60.Cb Numerical simulation; solution of equations

MSC

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Computational physics

Dates

Issue 1 (February 1999)

Received 17 November 1998



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