This article is cited in 8 papers

Calogero–FranÇoise Flows and Periodic Peakons

R. Beals^a, D. H. Sattinger^b, J. Szmigielski<sup>c

a</sup> Yale University
^b Utah State University
^c University of Saskatchewan

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.

DOI: 10.4213/tmf404

 English version: Theoretical and Mathematical Physics, 2002, 133:3, 1631–1646

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