  The dependence of physical properties of the electrically charged two-poles
monopole-antimonopole pair (MAP) solutions in the Higgs self-coupling constant
is previously investigated. In this paper we study the three-poles
monopole-antimonopole chain (MAC) solutions. The study includes $\phi$-winding
number $n=2,3,4$, and $5$. For the case of $n=2$, there is no bifurcating
branch along with the fundamental solution. Also no transition happens for this
solution for the Higgs self-coupling interval of $0\leq \lambda \leq 144$. For
the case of $n=3$, two transitions happen along the fundamental solution. Also
at a higher energy, there are two bifurcating branches. The lower energy branch
of these bifurcating branches, merges with the fundamental solution and both
terminate at the convergence point and do not survive for larger values of
$\lambda$. For $n=4$, a bifurcation is observed at higher energy in comparison
with the fundamental solution. Here there are three transitions. One is
observed along the fundamental solution and the others happen along the higher
energy bifurcating branch. For the case of $n=5$, the pattern is more complex.
A bifurcation in $\lambda = \lambda_{b1}$ happens with a higher energy than the
fundamental solution. A second bifurcation is observed at $\lambda =
\lambda_{b2}$. The two branches of the second bifurcation are both very close
in energy to the lower energy branch of the first bifurcation, but they have
different electrical and geometrical properties. Therefore, for the case of
$n=5$, we have three distinct solution for the interval of $\lambda_{b1}\leq
\lambda \leq \lambda_{b2}$ and five distinct solutions for $\lambda_{b2}\leq
\lambda \leq 300$. Also two transitions are observed in the higher energy
branch of the first bifurcation.

High Energy Physics - Theory