Multicomponent coherently coupled and incoherently coupled solitons and their collisions

TL;DR

This paper studies multicomponent coherently and incoherently coupled solitons in nonlinear Schrödinger equations, revealing complex collision behaviors, energy sharing, and potential applications in optical computing.

Contribution

It introduces a non-standard Hirota bilinearization method to derive general soliton solutions and classifies solitons based on their coupling, analyzing their collision dynamics in multicomponent systems.

Findings

Coherently coupled solitons undergo energy switching during collisions.

Incoherently coupled solitons exhibit elastic collisions for m=2.

For m>2, incoherently coupled solitons show energy sharing and complex collision behavior.

Abstract

We consider the integrable multicomponent coherently coupled nonlinear Schr\"odinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr type nonlinear media. The correct bilinear equations of $m$-CCNLS equations are obtained by 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, by obtaining the more general two-soliton solutions using this non-standard bilinearization approach we demonstrate that the collision among coherently coupled soliton and incoherently coupled soliton displays a non-trivial collision 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 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.