Deformations and Nonlinear Systems

Abstract

The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schrödinger equation are considered. The procedure is generalized to broader class of nonlinearities related to other types of deformations. The nonlinear noncanonical transforms used in the deformation procedure are shown to preserve in some cases the linear dynamical equations, for instance, for the harmonic oscillators. The nonlinear coherent states and some physical aspects of the deformations are reviewed.

23 pages,LATEX, to be published in Rend.Sem.Mat.Univ.Polit.Torino, volume 54 (1996), as Proceedings of Workshop on "Geometry and Plysics" Vietri Sept.29 1996, (S.Benenti, G.Marmo, A.Simoni, Eds.)