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A generalisation of the Calogero-Moser system. (English) Zbl 0587.70013

The authors introduce and solve exactly, a generalization of the many- body system of Calogero-Moser type [e.g.: J. Moser, Adv. Math. 16, 197-220 (1975; Zbl 0303.34019)], in which the particles, being free to move in complex plane, possess internal degrees of freedom. The method of M. A. Olshanetsky and A. M. Perelomov [e.g.: Lett. Nuovo Cimento 17, 97 ff. (1976)] is applied. The systems are shown to have a series of conservation laws, and among them there are enough integrals for the equations to be completely integrable.
Reviewer: Ju.Je.Gliklich

MSC:

70H05 Hamilton’s equations
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Citations:

Zbl 0303.34019
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References:

[1] Calogero, F., J. Math. Phys., 12, 419 (1971)
[2] Moser, J., Adv. Math., 17, 197 (1975)
[3] Olshanetsky, M. A.; Perelomov, A. M., Lett. Nuovo Cimento, 16, 333 (1976)
[4] Airault, H.; McKean, H. P.; Moser, J., Comm. on Pure and Applied Math., vol. 30, 95 (1977) · Zbl 0338.35024
[5] Calogero, F.; Degasperis, A., Lett. Nuovo Cimento, 16, 425 (1976)
[6] Adler, M., J. Math. Phys., 20, 60 (1979)
[7] Arnold, V. I., Mathematical Methods of Classical Mechanics, ((1978), Springer: Springer New York), 371, appendix 4
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