Strongly non-linear oscillators with slowly varying parameters

A multiple scales method, which gives the approximate solution in terms of elliptic functions, is used for the study of strongly non-linear oscillators with slowly varying parameters. As an application, quadratic and cubic non-linear oscillators are studied in detail. Two examples are considered: a generalized Van der Pol oscillator and a pendulum with variable length. Comparisons are also made with numerical results to show the efficiency of the present method.