Localized Structures in Dissipative Nonlinear Systems - Abstract
Bugaychuk, Svitlana
Spatial localized structures of the intensity pattern are formed via degenerate four-wave mixing in bulk nonlocal media. The nonlocal response leads to phase delay between interacted waves that resulting to localized pattern, which has a distribution of the intensity in a form similar to either the bright or the dark soliton. We found the transformation of the initial system consisted of five complex equations to one complex Ginzburg Landau equation by applying the reductive perturbation method. It is determined initial condition areas both for stable localized structures and for unstable ones. Unstable localized structures turn into periodic oscillations when one applies a white noise to a system. These features of the wave coupling may find applications for signal processing. They predict transmission of moving localized patterns in fibers.