Vector peregrine composites on the periodic background in spin–orbit coupled Spin-1 Bose–Einstein condensates

Abstract

Vector Gross–Pitaevskii system in spin–orbit coupled Spin-1 Bose–Einstein condensates is simplified into Manakov system. By means of the nonrecursive Darboux method, vector Peregrine solutions were given, including first-order and second-order vector Peregrine solutions with four structural parameters. From these solutions, vector peregrine composites on the periodic background are found by modulating the magnitudes of four structural parameters, including first-order and second-order Peregrine structures on the periodic background, and Peregrine doublets and Peregrine “three sisters” on the periodic background. The influence of the wave number and amplitude parameters on the first-order and second-order Peregrine structures on the periodic background for three components is studied. These results will provide a deeper understanding of nonlinear wave phenomena in spin–orbit coupled Spin-1 Bose–Einstein condensates.