Spatially modulated two- and three-component Rabi-coupled Gross–Pitaevskii systems

Abstract

Vector rogue wave (RW) formation and its dynamics in Rabi-coupled two- and three-species Bose–Einstein condensates with spatially varying dispersion and nonlinearity are studied. For this purpose, we obtain the RW solution of the two- and three-component inhomogeneous Gross–Pitaevskii (GP) systems with Rabi coupling by introducing suitable rotational and similarity transformations. Then, we investigate the effect of inhomogeneity (spatially varying dispersion, trapping potential and nonlinearity) on vector RWs for two different forms of potential strengths, namely periodic (optical lattice) with specific reference to hyperbolic-type potentials and parabolic cylinder potentials. First, we show an interesting oscillating boomeronic behaviour of dark–bright solitons due to Rabi coupling in two-component condensate with constant nonlinearities. Then in the presence of inhomogeneity but in the absence of Rabi coupling we demonstrate the creation of new daughter RWs co-existing with a dark (bright) soliton part in the first (second) component of the two-component GP system. Further, the hyperbolic modulation (sech type) of the parameter along with the Rabi effect leads to the formation of dromion (two-dimensional localized structure) trains even in the (1 + 1) dimensional two-component GP system, which is a striking feature of Rabi coupling with spatial modulation. Next, our study on three-component condensate reveals the fact that the three RWs can be converted into broad-based zero-background RW appearing on top of a bright soliton by introducing spatial modulation only. Further, by including Rabi coupling we observe beating behaviour of solitons with internal oscillations mostly at the wings. Also, we show that by employing parabolic cylinder modulation with model parameter n, one can produce RWs. Our explores that the spatially varying environment leads to the possibility of realization of a two-dimensional nonlinear structure in (1 + 1) dimensional setting.