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

## TL;DR

This paper investigates how spatial inhomogeneity and Rabi coupling influence rogue wave formation and dynamics in multi-component Bose-Einstein condensates, revealing novel localized structures and behaviors.

## Contribution

It introduces new solutions for inhomogeneous multi-component GP systems with Rabi coupling, demonstrating novel rogue wave phenomena and localized structures under spatial modulation.

## Key findings

- Rabi coupling causes oscillating dark-bright solitons in two components.
- Inhomogeneity leads to creation of daughter rogue waves coexisting with solitons.
- Hyperbolic modulation induces dromion train formation in two-component systems.

## Abstract

Vector rogue wave (RW) formation and their 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 creation of new daughter RWs co-existing with dark (bright) soliton part in first (second) component of the two-component GP system. Further, the hyperbolic modulation (sech type) of parameter along with 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 $(n+1)$ RWs.