Intermittent explosions of dissipative solitons and noise-induced crisis

Dissipative solitons show a variety of behaviors not exhibited by their conservative counterparts. For instance, a dissipative soliton can remain localized for a long period of time without major profile changes, then grow and become broader for a short time - explode - and return to the original spatial profile afterward. Here we consider the dynamics of dissipative solitons and the onset of explosions in detail. By using the one-dimensional complex Ginzburg-Landau model and adjusting a single parameter, we show how the appearance of explosions has the general signatures of intermittency: the periods of time between explosions are irregular even in the absence of noise, but their mean value is related to the distance to criticality by a power law. We conjecture that these explosions are a manifestation of attractor-merging crises, as the continuum of localized solitons induced by translation symmetry becomes connected by short-lived trajectories, forming a delocalized attractor. As additive noise is added, the extended system shows the same scaling found by low-dimensional systems exhibiting crises, thus supporting the validity of the proposed picture.