Transition between monopole and antimonopole for electrically charged monopole-antimonopole chain system of solutions

The dependence of physical properties of the electrically charged 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 ϕ-winding number n=2,3, and 4. For the case of n=2, no bifurcation and geometrical transition is detected for the interval of the study. For the case of n=3, two geometrical transitions happen along the fundamental solution. Also two bifurcations and one joining point is detected for the interval of study. The case of n=4 includes one bifurcation. There is also a geometrical transition along the fundamental solution and two transitions along the Higher energy bifurcating branch. This study implies that during some specific kind of geometrical transition, a magnetic and electric charge transition occurs for the pole which is located at the origin.