  We show that manifest superfluid properties of the Minkowskian Higgs model
with vacuum BPS monopoles quantized by Dirac may be described in the framework
of the Cauchy problem to the Gribov ambiguity equation.
  The latter equation specifies the ambiguity in choosing the covariant Coulomb
(transverse) gauge for Yang-Mills fields represented as topological Dirac
variables, may be treated as solutions to the Gauss law constraint at the
removal of temporal components of these fields.
  We demonstrate that the above Cauchy problem comes just to fixing the
covariant Coulomb gauge for topological Dirac variables in the given initial
time instant $t_0$ and finding the solutions to the Gribov ambiguity equation
in the shape of vacuum BPS monopoles and excitations over the BPS monopole
vacuum referring to the class of multipoles.
  The next goal of the present study will be specifying the look of Gribov
topological multipliers entering Dirac variables in the Minkowskian Higgs model
quantized by Dirac, especially at the spatial infinity, $| {\bf x} | \to
\infty$ (that corresponds to the infrared region of the momentum space).
