Dynamics and collisions of moving solitons in Bragg gratings with dispersive reflectivity

Results of systematic investigation of the stability of moving solitons and soliton-soliton collisions are reported within the framework of the recently proposed model which is a generalization of the standard model of fiber Bragg gratings (BGs). The new model takes into account dispersion of the Bragg reflectivity, which is relevant for the description of novel optical media, such as BGs on photonic wires, Bragg superstructures, periodic composite waveguides, etc. The stability analysis for moving solitons is necessary because experimental methods create only sufficiently fast solitons in fiber BGs. We demonstrate that the dispersive reflectivity expands the stability region for the solitons, while unstable solitons are transformed into persistent breathers. The parameter region which admits the merger of colliding solitons into a single one also gets much broader under the action of the dispersive reflectivity, and new outcomes of the collision become possible, which are absent in the standard BG model: elastic bounce of the solitons and an inelastic reaction generating three solitons out of two.