  We demonstrate spontaneous generation of spatially-periodic supersolid-like
super-lattice and stripe solitons in Rashba spin-orbit (SO) coupled spin-1 and
spin-2 quasi-two-dimensional nonmagnetic Bose-Einstein condensates (BECs). The
solitons in a weakly SO-coupled spin-1 BEC are circularly-symmetric of $(-1, 0,
+1)$ and $(0, +1, +2)$ types and have inherent vorticity; the numbers in the
parentheses are the winding numbers in hyper-spin components $+1, 0, -1$,
respectively. The circularly-symmetric solitons in an SO-coupled spin-2 BEC are
of types $(-2, -1, 0, +1, +2)$ and $(-1, 0, +1, +2, +3)$ with the former being
the ground state, where the winding numbers correspond to spin components $+2,
+1, 0, -1, -2$, respectively. For stronger SO-coupling strengths, these
solitons acquire a multiring structure while preserving the winding numbers.
Quasi-degenerate stripe and super-lattice solitons, besides a
circularly-asymmetric soliton, also emerge as excited stationary states for
stronger SO-coupling strengths in spin-1 and spin-2 BECs. pla-cl.tex
