On the back-firing instability

The onset of the back-firing instability is studied in a one-dimensional spatially extended and dissipative system, where propagating localized solutions become unstable. It corresponds to the emission in the tail of a solitary wave of a new wave propagating in the opposite direction. We describe in geometrical term the transition, using a normal form equation as example. We relate the instability scenario to a mechanism of spatio-temporal chaos