Skyrmion and Baby Skyrmion Formation from Domain Walls

We numerically simulate the formation of $(2+1)$-dimensional baby Skyrmions and $(3+1)$-dimensional $SU(2)$ Skyrmions from domain wall collisions. It has been suggested that Skyrmion, anti-Skyrmion pairs can be produced from the interaction of two domain walls. This is confirmed, however it is also demonstrated that the process can require quite precise conditions. An alternative, more stable, formation process is proposed as the interaction of more than two segments of domain wall. This is simulated, requiring far less constraints on the initial conditions used. Finally domain wall networks are considered, demonstrating how Skyrmions may be produced in a complex dynamical system. We show that the local topological charge configurations, formed within the system, are countered by opposite winding on the boundary of the system to conserve topological charge.