  We numerically demonstrate two-dimensional (2D) matter-wave solitons in the
disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly
anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are
square lattices which can be formed by interfering two pairs of plane waves
with different intensities. The hopping rates of the condensates between two
adjacent lattices in the orthogonal directions are different, which gives rise
to a linearly anisotropic system. We find that when the polarized orientation
of the dipoles is parallel to disk's plane with the same direction, the
combined effects of the linearly anisotropy and the nonlocal nonlinear
anisotropy strongly influence the formations, as well as the dynamics of the
lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found
when these combined effects reach a balance. Motion, collision and rotation of
the IPSs are also studied in detail by means of systematic simulations. We
further find that these IPSs can move freely in the 2D anisotropic discrete
system, hence giving rise to an anisotropic effective mass. Four types of
collisions between the IPSs are identified. By rotating an external magnetic
field up to a critical angular velocity, the IPSs can still remain localized
and play as a breather. Finally, the influences from the combined effects
between the linear and the nonlocal nonlinear anisotropy with consideration of
the contact/local nonlinearity are discussed too.
