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 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 copropagating modes/components. Further, the more general two-soliton solutions are obtained by using this non-standard bilinearization approach and various fascinating collision dynamics are pointed out. Particularly, we demonstrate that the collision among coherently coupled soliton and incoherently coupled soliton displays a nontrivial 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.

Novel energy sharing collisions of multicomponent solitons

“…The exact forms of g (j) , f , and s, which result in the soliton solutions of (5), are obtained by suitably expressing them as power series and recursively solving the resulting set of equations at various powers of expansion parameter from the bilinear equations (6). One can refer to [23] for more details regarding the soliton solutions of (5).…”

Wide vector solitons in systems with time- and space-modulated nonlinearities

“…Such kinds of bright flat-top solitons have also been reported in nonintegrable complex Ginzburg-Landau equations [37]. We think that a generalization of [36] to coherently coupled (nonautonomous) NLSEs may be possible and it will be considered in the near future.…”

“…Moreover, we would like to mention an interesting work dealing with multicomponent coupled solitons described by coherently coupled (autonomous) NLSEs [36]. In one specific case treated in that work, a bright-bright vector soliton solution, with one of the components exhibiting a flat-top profile very similar to 2 2 shown in Fig.…”

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

“…For example, Kanna and Sakkaravarthi [52] investigated the integrable N-component coherently coupled NLS equations describing simultaneous propagation of multiple fields in Kerr-type nonlinear media by 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. So in this appendix, we will extend the results in the paper to three-dimensional N-coupled NLS equations and present the similarity transformations for them: for…”