On the sensitivity of strongly nonlinear autonomous oscillators and oscillatory waves to small perturbations

Original asymptotic solutions are determined for two autonomous differential equations. The application of initial conditions for the energy, wave number and phase shift proves to be less complicated than in previous work. For the damped simple pendulum, explicit solutions demonstrate the dependence on the initial conditions. For strongly nonlinear wave packets of the Klein-Gordon equation, asymptotic solutions are compared. In both cases, the phase shift is shown to be highly sensitive to small perturbations in the initial conditions.