Geodesic
Calogero--Fran\c{C}oise Flows and Periodic Peakons
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 367-385

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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. 
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     author = {R. Beals and D. H. Sattinger and J. Szmigielski},
     title = {Calogero--Fran\c{C}oise {Flows} and {Periodic} {Peakons}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a3/}
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R. Beals; D. H. Sattinger; J. Szmigielski. Calogero--Fran\c{C}oise Flows and Periodic Peakons. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 367-385. http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a3/