NONLINEAR INSTABILITIES RELATING TO NEGATIVE-ENERGY MODES

The nonlinear instability of general linearly stable systems allowing linear negative-energy perturbations is investigated with the aid of a multiple-time-scale formalism. It is shown that the basic equations t hus obtained imply resonance conditions and possess inherent symmetrie s which lead to the existence of similarity solutions of these equatio ns. These solutions can be of an explosive type, oscillatory, or stati c. It is demonstrated that at least some of the oscillatory and static solutions are normally linearly unstable.