(2+1)-dimensional unstable matter waves in self-interacting pseudospin-1/2 BECs under combined Rashba and Dresselhaus spin-orbit couplings

Abstract

The modulational instability (MI) of continuous waves is exclusively addressed theoretically and numerically in a two-component Bose-Einstein condensate in the presence of a mixture of Rashba and Dresselhaus (RD) spin-orbit couplings and the Lee-Huang-Yang (LHY) term. The linear stability analysis is utilized to derive an expression for the MI growth rate. It is revealed that instability can be excited in the presence of the RD spin-orbit coupling under conditions where nonlinear and dispersive effects are suitably balanced. Analytical predictions are confirmed via direct numerical simulations, where MI is manifested by the emergence of soliton-molecules that include four-peaked solitons and more exotic vortex structures that are very sensitive to variations in spin-orbit coupling strengths. Our study suggests that MI is a suitable mechanism for generating matter waves through multi-peaked solitons of various geometries.