Soliton junctions in the large magnetic flux limit

We study the flux tube junctions in the limit of large magnetic flux. In this limit the flux tube becomes a wall vortex which is a wall of negligible thickness (compared to the radius of the tube) compactified on a cylinder and stabilized by the flux inside. This wall surface can also assume different shapes that correspond to soliton junctions. We can have a flux tube that ends on a wall, a flux tube that ends on a monopole and more generic configurations containing all three of them. In this paper we find the differential equations that describe the shape of the wall vortex surface for these junctions. We will restrict to the cases of cylindrical symmetry. We also solve numerically these differential equations for various kinds of junctions. We finally find an interesting relation between soliton junctions and dynamical systems.