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We develop stability analysis for matter-wave solitons in a two-dimensional (2D) Bose-Einstein condensate loaded in an optical lattice (OL), to which periodic time modulation is applied, in different forms. The stability is studied by dint of the variational approximation and systematic simulations. For solitons in the semi-infinite gap, well-defined stability patterns are produced under the action of the attractive nonlinearity, clearly exhibiting the presence of resonance frequencies. The analysis is reported for several time-modulation formats, including the case of in-phase modulations of both quasi-1D sublattices, which build the 2D square-shaped OL, and setups with asynchronous modulation of the sublattices. In particular, when the modulations of two sublattices are phase-shifted by {delta}={pi}/2, the stability map is not improved, as the originally well-structured stability pattern becomes fuzzy and the stability at high modulation frequencies is considerably reduced. Mixed results are obtained for anti-phase modulations of the sublattices ({delta}={pi}), where extended stability regions are found for low modulation frequencies, but for high frequencies the stability is weakened. The analysis is also performed in the case of the repulsive nonlinearity, for solitons in the first finite bandgap. It is concluded that, even though stability regions may be found, distinct stability boundaries for the gap solitons cannot be identified clearly. Finally, the stability is also explored for vortex solitons of both the square-shaped and rhombic types (i.e., off- and on-site-centered ones).
We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we
We investigate dynamics of two-dimensional chiral solitons of semi-vortex (SV) and mixed-mode (MM) types in spin-orbit-coupled Bose-Einstein condensates with the Manakov nonlinearity, loaded in a dual-core (double-layer) trap. The system supports two
We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov-de Gennes equations both numerically and analytically, we find that the stability problem effectively
We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making the relativ
It was recently found that, under the action of the spin-orbit coupling (SOC) and Zeeman splitting (ZS), binary BEC with intrinsic cubic nonlinearity supports families of gap solitons, provided that the kinetic energy is negligible in comparison with