Modulational instability in two-dimensional dissipative open Bose-Einstein condensates with mixed helicoidal and Rashba-Dresselhaus spin-orbit couplings

The letter proposes a modified set of coupled two-dimensional (2D) cubic complex Ginzburg-Landau (CGL) equations that include Rashba and Dresselhaus as well as helicoidal spin-orbit couplings (SOCs) and further study matter-wave formation using modulational instability (MI) in 2D Bose-Einstein condensates (BECs). Analytically, the linear stability analysis proposes an expression for the MI gain. The subsequent parametric study explores the effects of the included SO coupling, principally the competition involving the Rashba-Dresselhaus (RD) SOCs and the helicoidal SOC. Numerically, analytical predictions are confirmed through the emergence of dissipative nonlinear patterns under a suitable balance of the competing SOC terms, manifested by the disintegration of the continuous waves in a broad range of structures under effective energy exchange between the two BEC components. Combining dissipative effects and SOC in a 2D context extends the class of physical models that can investigate various suitable wave patterns in binary BECs. •Matter-wave formation using modulational instability in 2D dissipative open Bose-Einstein condensates is studied.•The presence of competing Rashba, Dresselhaus, and helicoidal spin-orbit couplings impacts the distribution of parameter domains.•The interplay between the spin-orbit coupling gives rise to dissipative solitons through direct numerical simulations.•New wave patterns are induced by the annihilation/recombination process as part of energy exchange between the two BEC species.