Sudden transition to spatiotemporal chaos in a nonlinear Klein–Gordon equation

We investigate the transition from modulational to spatiotemporally chaotic dynamics of a high-frequency continuous field governed by a nonlinear Klein–Gordon equation. A critical curve on the amplitude–frequency plane for the carrier exists such that a transition to spatiotemporal chaos becomes possible if the carrier frequency is smaller than the critical. Under this condition transition is sharply localized in time and occurs abruptly as the wave amplitude is raised. A low-dimensional truncation of the full system enables to understand the basic features.