Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
Copyright policy )Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
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 $t\rightarrow\infty$.
- University of Chicago United States
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, \(N\)-body problems, Nonlinear Sciences - Exactly Solvable and Integrable Systems, many-body problems, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Dynamical Systems (math.DS), \(n\)-body problems, N-body problems, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, isochronous systems, QA1-939, partial differential equations, FOS: Mathematics, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematics
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, \(N\)-body problems, Nonlinear Sciences - Exactly Solvable and Integrable Systems, many-body problems, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Dynamical Systems (math.DS), \(n\)-body problems, N-body problems, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, isochronous systems, QA1-939, partial differential equations, FOS: Mathematics, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematics
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