Collisions between discrete spatiotemporal Ginzburg-Landau solitons

Abstract

We report systematic results of collisions between discrete spatiotemporal Ginzburg-Landau solitons in waveguide arrays. Depending on the value of the kick parameter (collision momentum), four generic outcomes are identified in the case of collision of two identical solitons located at equal distances from the edge of the waveguide array: (a) merger of the solitons into a single one, at small values of the kick parameter, (b) creation of an extra soliton at intermediate values of the collision momentum, (c) quasi-elastic interactions at both intermediate values of the kick parameter (for relatively small values of the cubic gain) and at large values of the kick parameter (for relatively high values of cubic gain), and (d) soliton spreading at relatively large values of the collision momentum but only in the case of relatively small values of the cubic gain. In the case of collision of two non-identical solitons located at different distances from the edge of the waveguide array four generic outcomes were identified too: (e) soliton bouncing, accompanied by a sharp modification of soliton velocities during the interaction process, for relatively small values of the collision momentum, (f) soliton creation at intermediate values of the kick parameter and for relatively low values of the cubic gain, (g) soliton spreading (in time) at intermediate values of the collision momentum and for relatively high values of the cubic gain, and (h) quasi-elastic interactions at large values of the the kick parameter.