Phase transitions and dynamics of one-dimensional solitons in spin-orbit-coupled Bose-Bose mixtures

We investigate the formation, stability, and dynamics of solitons in a one-dimensional binary Bose-Einstein condensate under the action of the spin-orbit-coupling (SOC) and Lee-Huang-Yang (LHY) correction to the underlying system of the Gross-Pitaevskii equations. We identify the semi-dipole (SD) family of solitons and thoroughly analyze its properties. The numerical analysis reveals intricate bifurcations, including transitions from real to complex-valued stationary wavefunctions of the SD solitons and norm-dependent dynamical instabilities. Stability maps in the plane of the solitons' norm and interaction strength exhibit areas of monostability, oscillatory behavior, and soliton splitting. Solitons with complex stationary wavefunctions emerge as ground states in broad parameter areas, due to the effects of the LHY terms. The other soliton species, in the form of mixed modes (MMs), does not feature the compexification bifurcation. In the LHY-dominated regime, the SD and MM solitons exhibit identical values of the energy for the same norm. The results deepen the understanding of nonlinear matter-wave states and reveal multi-stable ones in quantum gases.