NORMALIZATION OF PERTURBED NONLINEAR HAMILTONIAN OSCILLATORS

We present a new way of handling perturbed non-linear oscillators. The solution of the equations of motion of a non-linear oscillator, gener ally, involves elliptic functions. The main key of our method consists in keeping these elliptic functions in the unperturbed part, and expa nding the perturbation as a Fourier series of the amplitude, in which coefficients are powers of the Jacobian nome. Once the Fourier expansi on is obtained, Lie based perturbation methods may be applied to it. A s an illustration, the hard Duffing oscillator perturbed by sextic ter m is considered. Comparisons between our method and the exact solution (that is given here) are carried out. (C) 1997 Elsevier Science Ltd.