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

Abstract

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.

30 pages, 2 figures

References in corpus (5)

• The Darboux transformation and algebraic deformations of shape-invariant potentials
• Supersymmetry and algebraic deformations
• Quasi-Exact Solvability and the direct approach to invariant subspaces
• Quasi-exact solvability beyond the SL(2) algebraization
• Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces

Cited by in corpus (1)

• Time-dependent polynomials with one multiple root and new solvable dynamical systems