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

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

2007-01-22

arxiv.org/abs/nlin/0701046v1

J. Phys. A 40 (2007), no. 20, 5335--5353

Nonlinear Sciences

Exactly Solvable and Integrable Systems

30 pages, 2 figures

Scientific paper

10.1088/1751-8113/40/20/007

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.

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