Transformation of a dark soliton into a bright pulse

We consider a system of cubic complex Ginzburg-Landau equations governing copropagation of two waves with opposite signs of the dispersion in a nonlinear optical fiber in the presence of gain and losses. The waves are coupled by cross-phase modulation and stimulated Raman scattering. A special exact solution for a bound state of bright and dark solitons is found (unlike the well-known exact dark-soliton solution to the single complex Ginzburg-Landau equation, which is a sink, this compound soliton proves to be a source emitting traveling waves). Numerical simulations reveal that the compound soliton remains stable over -10 soliton periods. Next, we demonstrate that a very weak seed noise, added to an initial state in the form of a dark soliton in the normal-dispersion mode and nothing in the anomalous-dispersion one, gives rise to a process of the generation of a bright pulse in the latter mode, while the dark soliton gets grayer and eventually disappears. Thus this scheme can be used for an effective transformation of a dark soliton into a bright one, which is of interest by itself and may also find applications in photonics.