Gibbons, John; Hermsen, Theo A generalisation of the Calogero-Moser system. (English) Zbl 0587.70013 Physica D 11, 337-348 (1984). 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 Cited in 1 ReviewCited in 72 Documents 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 Keywords:free motion in complex plane; generalization of the many-body system; internal degrees of freedom; conservation laws Citations:Zbl 0303.34019 PDFBibTeX XMLCite \textit{J. Gibbons} and \textit{T. Hermsen}, Physica D 11, 337--348 (1984; Zbl 0587.70013) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.