  The recent discovery of iron pnictide superconductors has resulted in a
rapidly growing interest in multiband models with more than two bands. In this
work we specifically focus on the properties of three-band Ginzburg-Landau
models which do not have direct counterparts in more studied two-band models.
First we derive normal modes and characteristic length scales in the
conventional U(1) three-band Ginzburg-Landau model as well as in its time
reversal symmetry broken counterpart with $U(1)\times Z_2$ symmetry. We show
that in the latter case, the normal modes are mixed phase/density collective
excitations. A possibility of the appearance of a massless phase-difference
mode associated with fluctuations of the phase difference is also discussed.
Next we show that gradients of densities and phase differences can be
inextricably intertwined in vortex excitations in three-band models. This can
lead to very long-range attractive intervortex interactions and appearance of
type-1.5 regimes even when the intercomponent Josephson coupling is large. In
some cases it also results in the formation of a domain-like structures in the
form of a ring of suppressed density around a vortex across which one of the
phases shifts by $\pi$. We also show that field-induced vortices can lead to a
change of broken symmetry from U(1) to $U(1)\times Z_2$ in the system. In the
type-1.5 regime, it results in a semi-Meissner state where the system has a
macroscopic phase separation in domains with broken U(1) and $U(1)\times Z_2$
symmetries.
