  Violation of non-Abelian Bianchi identity can be regarded as $N^2-1$
Abelian-like monopole currents in the continuum SU(N) QCD. Three Abelian-like
monopoles, when defined in SU(2) gluodynamics on the lattice \`{a} la
DeGrand-Toussaint, are shown to have the continuum limit with respect to the
color-invariant monopole density and the effective monopole action. Since each
Abelian-like monopole is not gauge invariant, we have introduced various
partial gauge fixing for the purpose of reducing lattice artifact monopoles in
the thermalized vacuum. Here we investigate Abelian and monopole dominances and
the Abelian dual Meissner effects adopting the same gauges like the maximal
center gauge (MCG) in comparison with the maximal Abelian gauge (MAG). Abelian
and monopole contributions to the string tension in these gauges are observed
to be a little smaller than the non-Abelian string tension. However, we find
that the monopole dominance is improved well when use is made of the block-spin
transformations with respect to Abelian-like monopoles. We find each electric
field is squeezed by the corresponding colored Abelian-like monopole in such
gauges and the Abelian dual Meissner effect is observed independently for each
color. Moreover, we confirm the dual Amp\`{e}re's law in these new gauges as
well as in MAG. The SU(2) vacuum is shown to be near the border between the
type 1 and type 2 dual superconductors. The penetration length is almost equal
for the four gauge fixings and the vacuum type in MCG is almost the same value
as the previous results. These results are consistent with the previous results
suggesting the continuum limit and the gauge-independence of Abelian monopoles.
