  We present an analysis of two-dimensional (2D) matter-wave solitons, governed
by the pseudo-spinor system of Gross-Pitaevskii equations with self- and
cross-attraction, which includes the spin-orbit coupling (SOC) in the general
Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman
splitting. Families of semi-vortex (SV) and mixed-mode (MM) solitons are
constructed, which exist and are stable in free space, as the SOC terms prevent
the onset of the critical collapse and create the otherwise missing ground
states in the form of the solitons. The Dresselhaus SOC produces a destructive
effect on the vortex solitons, while the Zeeman term tends to convert the MM
states into the SV ones, which eventually suffer delocalization. Existence
domains and stability boundaries are identified for the soliton families. For
physically relevant parameters of the SOC system, the number of atoms in the 2D
solitons is limited by $\sim 1.5\times 10^{4}$. The results are obtained by
means of combined analytical and numerical methods.
