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It is commonly known that two-dimensional mean-field models of optical andmatter waves with the cubic self-attraction cannot produce stable solitons infree space because of the occurrence of the collapse in the same setting. Bymeans of the numerical analysis and variational approximation, we demonstratethat the two-component model of the Bose-Einstein condensate, with thespin-orbit Rashba coupling and cubic attractive interactions, gives rise tosolitary-vortex complexes of two types: semi-vortices (SVs, with a vortex inone component and a fundamental soliton in the other), and mixed modes (MMs,with topological charges 0 and +1/-1 mixed in both components). These two-dimensional composite modes can be created using the trappingharmonic-oscillator (HO) potential, but remain stable in the free space, if thetrap is gradually removed. The SVs and MMs realize the ground state of thesystem, provided that the self-attraction in the two components is,respectively, stronger or weaker than the cross-attraction between them. TheSVs and MMs which are not the ground state are subject to a drift instability.In the free space (in the absence of the HO trap), modes of both typesdegenerate into unstable Townes solitons when their norms attain the respectivecritical values, while there is no lower existence threshold for the stablemodes. Moving free-space stable solitons are also found in the presentnon-Galilean-invariant system, up to a critical velocity. Collisions betweentwo moving solitons lead to their merger into a single one.

The creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space