Ermakov-Lewis invariants for a class of parametric anharmonic oscillators

Abstract In this letter, we investigate a general class of damped anharmonic oscillators with time-dependent coefficients. The model is a second-order ordinary differential equation in which the driving is a general function of the solution and time. Several well-known equations of mathematical physics are generalized by our model. The equation is presented then as a generalized Ray-Reid system, and an invariant of the Ermakov-Lewis type is derived next. Particular forms of this invariant are obtained for the classical harmonic oscillator and the Ermakov equation. In this form, this work opens the investigation on the determination of Ermakov-Lewis invariants of anharmonic systems.