Two novel classes of solvable many-body problems of goldfish type with constraints

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Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
© IOP Publishing Ltd. The results reported in this paper where obtained during a visit in October 2006 of one of us (DGU) to the Department of Physics of the University of Rome “La Sapienza”, performed in the context of the Collaboration Agreement among the University of Rome “La Sapienza” and the Universidad Complutense of Madrid. The research of DGU is supported in part by the Ramón y Cajal program of the Ministerio de Ciencia y Tecnología and by the DGI under grants FIS2005-00752 and MTM2006-00478. It is a pleasure to acknowledge illuminating discussions with Robert Milson.
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