Multicomponent coherently coupled and incoherently coupled solitons and their collisions

Abstract

We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr-type nonlinear media. The correct bilinear equations of m-CCNLS equations are obtained using a non-standard type of Hirota's bilinearization method, and the more general bright one solitons with single-hump and double-hump profiles including special flat-top profiles are obtained. The solitons are classified as coherently coupled solitons and incoherently coupled solitons depending upon the presence and absence of coherent nonlinearity arising due to the existence of the co-propagating modes/components. Further, the more general two-soliton solutions are obtained using this non-standard bilinearization approach, and various fascinating collision dynamics are pointed out. Particularly, we demonstrate that the collision between coherently coupled solitons and incoherently coupled solitons displays a non-trivial behaviour in which the former always undergoes energy switching accompanied by an amplitude-dependent phase-shift and change in the relative separation distance, leaving the latter unaltered. But the collision between coherently coupled solitons alone is found to be a standard elastic collision. Our study also reveals the important fact that the collision between incoherently coupled solitons arising in the m-CCNLS system with m = 2 is always elastic, whereas for m > 2 the collision becomes intricate, and for this case the m-CCNLS system exhibits interesting energy-sharing collision of solitons characterized by intensity redistribution, amplitude-dependent phase-shift and change in relative separation distance, which is similar to that of the multicomponent Manakov soliton collisions. This suggests that the m-CCNLS system can also be a suitable candidate for soliton collision-based optical computing in addition to the Manakov system.