A Method of Solution for Resonant Nonlinear Coupled Oscillator Systems

Abstract

A method of solution for coupled oscillator systems having commensurable frequencies ω_k = kω and suitable nonlinear couplings is presented. The method is that of perturbation expansions about periodic solutions. For simplicity, a three‐oscillator system is discussed, but larger systems may be treated in the same way. The method provides results which are considerably better than those obtainable by any other currently available method, such as the perturbation method of Wigner‐Brillouin. As presented, the method is rather unrefined, but it demonstrates that nonlinear oscillator systems of this resonant type are susceptible to analysis.