Soliton interaction and further merging in normal-dispersion fiber lasers modeled with the cubic-quintic CGLE

We study the interaction and merging of optical solitons in normal-dispersion fiber lasers within the framework of the cubic-quintic complex Ginzburg Landau equation (CGLE). We start finding homogeneous analytic solutions to this equation that are used in numerical simulations to build interacting kinks that lead to the formation of stable solitons. We then study numerically the interaction and merging of these solitons and characterize this process using moments such as the energy and momentum along the fiber. We have found that the merging process occurs only for small enough values of the initial distance (that depends on the phase difference) between solitons, otherwise they repel each other monotonically. The structure of the merging process shows a double peaked energy burst and (depending on the phase difference) a gain and/or loss of momentum. Finally, we propose a fitting model for isolated solitons in order to find a suitable analytical representation for the attractive interaction law before their merging.