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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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\paper Calogero--Fran\c{C}oise Flows and Periodic Peakons
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\issue 3
\pages 367--385
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\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 3
\pages 1631--1646
\crossref{https://doi.org/10.1023/A:1021358107495}
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  • https://www.mathnet.ru/eng/tmf/v133/i3/p367
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :202
    References:36
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