Collisional dynamics of solitons in the coupled PT symmetric nonlocal nonlinear Schrödinger equations

Abstract

We investigate the focussing coupled PT symmetric nonlocal nonlinear Schrödinger equation employing Darboux transformation approach. We find a family of exact solutions including pairs of Bright-Bright, Dark-Dark and Bright-Dark solitons in addition to solitary waves. We show that one can convert bright bound state onto a dark bound state in a two soliton solution by selectively finetuning the amplitude dependent parameter. We also show that the energy in each mode remains conserved unlike the celebrated Manakov model. We also characterize the behaviour of the soliton solutions in detail. We emphasize that the above phenomenon occurs due to the nonlocality of the model.

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

“…Another interesting impact of FWM on the nonlocal coupled NLSE is that it destroys the sensitivity to the parameter b 1 . In other words, we found earlier [28] that the manipulation of the different classes of soliton solutions such as B-B, B-D, D-B, D-D solitons can be performed sensitively by the parameter b 1 . The inclusion of FWM parameters in the model makes the free parameter b 1 a passive member in the group of parameters, which means the change of b 1 arbitrarily will not affect the density of the profiles shown in Fig.…”

“…With no FWM, the higher order solitonic solutions are shown to be a pair of B-B, D-D, or B-D solitons [28]. For completeness, and to show the effect of FWM, we present these solutions here, which may be obtained from Eq.…”

PT-symmetric KdV Solutions and Their Algebraic Extension with Zero-Width Resonances

“…Non-linear systems possessing PT -symmetry have been the subject of many recent investigations [18][19][20][21][22][23] . The effect of non-linearity on PT -symmetric potentials has been shown to lead to self-trapped modes 24,25 .…”