  We study supersolid-like states in a quasi-two-dimensional trapped Rashba and
Dresselhaus spin-orbit (SO) coupled spin-1 condensate. For small strengths of
SO coupling $\gamma$ ($\gamma \lessapprox 0.75$), in the ferromagnetic phase,
circularly-symmetric $(0,\pm 1, \pm 2)$- and $(\mp 1, 0,\pm 1)$-type states are
formed where the numbers in the parentheses denote the angular momentum of the
vortex at the center of the components and where the upper (lower) sign
correspond to Rashba (Dresselhaus) coupling; in the antiferromagnetic phase,
only $(\mp 1, 0,\pm 1)$-type states are formed. For large strengths of SO
coupling, supersolid-like superlattice and superstripe states are formed in the
ferromagnetic phase. In the antiferromagnetic phase, for large strengths of SO
coupling, supersolid-like superstripe and multi-ring states are formed. For an
equal mixture of Rashba and Dresselhaus SO couplings, only a superstripe state
is found. All these states are found to be dynamically stable and hence
accessible in an experiment and will enhance the fundamental understanding of
crystallization onto spatially periodic states in solids.
