Perturbation theory for dark-bright solitons of the Manakov system

We present a direct perturbation method to study the dynamics of dark-bright (DB) solitons of the Manakov system under the influence of perturbations. Our methodology combines a multi-scale expansion method, perturbed conservation laws and a boundary-layer approach, which breaks the problem into an inner region, pertinent to the soliton core and an outer region, which evolves independently of the dark-bright soliton. We find that a shelf emerges around the dark soliton component, which propagates with a speed depending on the background intensity. Conserved quantities of the Manakov system are employed to determine the properties of the perturbed solutions. We focus on dissipative perturbations, such as diffusion, as well as linear and nonlinear loss, and show that the effect of the bright (filling) soliton component is to partially stabilize 'bare' dark solitons of the scalar case against perturbation-induced dissipation. Our analytical predictions are corroborated by results of direct numerical simulations.