1999
DOI: 10.1088/0266-5611/15/1/001
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Multi-peakons and a theorem of Stieltjes

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.

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Cited by 260 publications
(303 citation statements)
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“…As well as in the present system, in that equation the peakons coexist with regular solitons [20]. In the next subsection, we demonstrate that the peakons, which are found only as limit-form solutions in the no-SPM case σ 3 = 0, become generic solutions in the case σ 3 = 0.…”
Section: (B)supporting
confidence: 69%
See 1 more Smart Citation
“…As well as in the present system, in that equation the peakons coexist with regular solitons [20]. In the next subsection, we demonstrate that the peakons, which are found only as limit-form solutions in the no-SPM case σ 3 = 0, become generic solutions in the case σ 3 = 0.…”
Section: (B)supporting
confidence: 69%
“…shows that the cuspons look like peakons; that is, except for the above-mentioned narrow region of the width |x| ∼ κ 2 , where the cusp is located, they have the shape of a soliton with a discontinuity in the first derivative of S(x) and a jump in the phase φ(x), which are the defining features of peakons ( [17,20]). …”
Section: Cuspons the Case σ 3 =mentioning
confidence: 99%
“…The system for N = 2 peakons is (we assume that x 1 < x 2 for all y and t, i.e. the case for which the N -peakon solution for the CH equation is obtained in [22,23]…”
Section: Peakon Solutions Of a (1+2) -Dimensional Equation From The Cmentioning
confidence: 99%
“…The CH solitary waves are stable solitons if ω > 0 [6,12,13,21] or peakons if ω = 0 [1,22,23]. The KdV and CH equations can also be interpreted as geodesic flow equations for the respective L 2 and H 1 metrics on the Bott-Virasoro group [24,25,26,27,28,29].…”
Section: Introductionmentioning
confidence: 99%
“…The N -peakon solutions (1.4) are weak solutions with discontinuous first derivatives at the positions q j of the peaks; q j , p j are canonical coordinates and momenta in an integrable finite-dimensional Hamiltonian system; the interpretation of weak solutions is discussed further in [12]. The N -peakon interaction was obtained in [3], with the explicit peakon-antipeakon interaction being given in [4]. The stability of peakons in the Camassa-Holm equation was proved in [13,14].…”
Section: Introductionmentioning
confidence: 99%