Bright–dark Peregrine solutions in helicoidal spin–orbit coupled Bose–Einstein condensates

Abstract

Vector Gross–Pitaevskii system in helicoidal spin–orbit coupled Bose–Einstein condensates can be reduced into vector nonlinear Schrödinger system. Employing the nonrecursive Darboux method, we find bright–dark Peregrine solutions, such as first-order and second-order vector Peregrine solutions, including vector Peregrine “three sisters” solutions. These results will provide a deeper understanding of nonlinear wave phenomena in helicoidal spin–orbit coupled Bose–Einstein condensates.