  Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii
equations with the repulsive nonlinearity and a potential of the
quasicrystallic type are constructed (in the 2D case, the potential corresponds
to a five-fold optical lattice). Stable 1D solitons in the weak potential are
explicitly found in three bandgaps. These solitons are mobile, and they collide
elastically. Many species of tightly bound 1D solitons are found in the strong
potential, both stable and unstable (unstable ones transform themselves into
asymmetric breathers). In the 2D model, families of both fundamental and
vortical solitons are found and are shown to be stable.
