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This article is cited in 8 scientific papers (total in 8 papers)
Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
Oksana Bihuna, Francesco Calogerob a Department of Mathematics, Concordia College at Moorhead, MN, USA
b Physics Department, University of Rome "La Sapienza", Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy
Abstract:
The class of solvable many-body problems “of goldfish type” is extended by including (the additional presence of) three-body forces. The solvable $N$-body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary “coupling constants”. Restrictions on these constants are identified which cause these systems — or appropriate variants of them — to be isochronous or asymptotically isochronous, i.e. all their solutions to be periodic with a fixed period (independent of the initial data) or to have this property up to contributions vanishing exponentially as $t\rightarrow \infty $.
Keywords:
many-body problems; $N$-body problems; partial differential equations; isochronous systems.
Received: June 7, 2013; in final form October 2, 2013; Published online October 9, 2013
Citation:
Oksana Bihun, Francesco Calogero, “Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces”, SIGMA, 9 (2013), 059, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma842 https://www.mathnet.ru/eng/sigma/v9/p59
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Abstract page: | 240 | Full-text PDF : | 45 | References: | 35 |
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