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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 3, Pages 367–385
DOI: https://doi.org/10.4213/tmf404 (Mi tmf404) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Calogero–FranÇoise Flows and Periodic Peakons

R. Bealsa, D. H. Sattingerb, J. Szmigielskic

a Yale University
b Utah State University
c University of Saskatchewan
Full-text PDF (280 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf404
Abstract: The completely integrable Hamiltonian systems discovered by Calogero and FranÇoise contain the finite-dimensional reductions of the Camassa–Holm and Hunter–Saxton equations. We show that the associated spectral problem has the same form as that of the periodic discrete Camassa–Holm equation. The flow is linearized by the Abel map on a hyperelliptic curve. For two-particle systems, which correspond to genus-1 curves, explicit solutions are obtained in terms of the Weierstrass elliptic functions.
Keywords: finite-dimensional Hamiltonians, elliptic and hyperelliptic curves, Abel maps.
English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 3, Pages 1631–1646
DOI: https://doi.org/10.1023/A:1021358107495
Bibliographic databases:
Language: Russian
Citation: R. Beals, D. H. Sattinger, J. Szmigielski, “Calogero–FranÇoise Flows and Periodic Peakons”, TMF, 133:3 (2002), 367–385; Theoret. and Math. Phys., 133:3 (2002), 1631–1646
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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  • https://www.mathnet.ru/eng/tmf404
  • https://doi.org/10.4213/tmf404
  • https://www.mathnet.ru/eng/tmf/v133/i3/p367
    • This publication is cited in the following 7 articles:
    1. Zhi Zhang, Xun Wang, “Sharp estimates of lowest positive Neumann eigenvalue for general indefinite Sturm-Liouville problems”, Journal of Differential Equations, 382 (2024), 302  crossref
    2. Jifeng Chu, Gang Meng, Zhi Zhang, “Minimizations of positive periodic and Dirichlet eigenvalues for general indefinite Sturm-Liouville problems”, Advances in Mathematics, 432 (2023), 109272  crossref
    3. Hans Lundmark, Jacek Szmigielski, “A view of the peakon world through the lens of approximation theory”, Physica D: Nonlinear Phenomena, 440 (2022), 133446  crossref
    4. Eckhardt J., Kostenko A., “The Inverse Spectral Problem For Periodic Conservative Multi-Peakon Solutions of the Camassa-Holm Equation”, Int. Math. Res. Notices, 2020:16 (2020), 5126–5151  crossref  mathscinet  isi
    5. Eckhardt J., Kostenko A., Nicolussi N., “Trace Formulas and Continuous Dependence of Spectra For the Periodic Conservative Camassa-Holm Flow”, J. Differ. Equ., 268:6 (2020), 3016–3034  crossref  mathscinet  isi  scopus
    6. Avan, J, “On Calogero-Franccediloise-type Lax matrices and their dynamical r-matrices”, Journal of Mathematical Physics, 50:7 (2009), 072701  crossref  mathscinet  adsnasa  isi  scopus  scopus
    7. Beals, R, “Periodic peakons and Calogero-Francoise flows”, Journal of the Institute of Mathematics of Jussieu, 4:1 (2005), 1  crossref  mathscinet  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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