349 citations · 1.5k across the 35 of their papers we have counts for
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A New Class of Solvable Many-Body Problems
Francesco Calogero, Ge Yi
A new class of solvable -body problems is identified. They describe unit-mass point particles whose time-evolution, generally taking place in the complex plane, is character…
Asymptotically isochronous systems
Francesco Calogero, David Gomez-Ullate
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent…
Two novel classes of solvable many-body problems of goldfish type with constraints
Francesco Calogero, David Gomez-Ullate
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…
Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces
David Gomez-Ullate, Niky Kamran, Robert Milson
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by poly…
Supersymmetry and algebraic deformations
D. Gomez-Ullate, N. Kamran, R. Milson
We describe a class of algebraically solvable SUSY models by considering the deformation of invariant polynomial flags by means of the Darboux transformation. The algebraic deforma…
Quasi-Exact Solvability and the direct approach to invariant subspaces
D. Gomez-Ullate, N. Kamran, R. Milson
We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of…