  We have focused in the paper on the most prominent and intensively studied
S=1 pseudospin formalism for extended bosonic Hubbard model (EHBM) with
truncation of the on-site Hilbert space to the three lowest occupation states n
= 0, 1, 2. The EHBM Hamiltonian is a paradigmatic model for the highly topical
field of ultracold gases in optical lattices. Generalized non-Heisenberg
effective pseudospin Hamiltonian does provide a deep link with boson system and
physically clear description of "the myriad of phases" from uniform Mott
insulating phases and density waves to two types of superfluids and
supersolids. We argue that the 2D pseudospin system is prone to a topological
phase separation and focus on several types of unconventional skyrmion-like
topological structures in 2D boson systems, which have not been analysed till
now. The structures are characterized by a complicated interplay of insulating
and the two superfluid phases with a single boson and two-boson condensation,
respectively.
