ABSTRACT
In this paper an overview is provided of an approach to identify systems of nonlinearly-coupled Ordinary Differential Equations solvable by algebraic operations— also including models interpretable as many-body problems with Newtonian equations of motion ("accelerations equal forces"). This technique—which was introduced several decades ago—has had an important evolution recently. This development entails that the universe of solvable models thereby generated is quite vast; it also includes dynamical systems which feature nontrivially rather simple time evolutions, for instance isochronous or asymptotically isochronous. In this paper this development is tersely described and representative examples of the solvable models thereby obtained are exhibited and tersely discussed. A differential algorithm to evaluate all the zeros of a generic polynomial of arbitrary degree is also reported. Extensions of this approach to systems of nonlinearly-coupled Partial Differential Equations and to evolutions in "discrete time" are tersely mentioned.
