  It is known that there exist solutions with interfaces to various scalar
nonlinear wave equations. In this paper, we look for solutions of a
two-component system of nonlinear wave equations where one of the components
has an interface and and where the second component is exponentially small
except near the interface of the first component. A formal asymptotic expansion
suggests that there exist solutions to this system with these characteristics
whose profiles are determined by the winding number density of the second
component and where the interface of the first component is a time-like surface
in Minkowski space whose geometric evolution is coupled in a highly nonlinear
way to the phase of the second component. We verify this heuristic when $n=2$
and for equivariant maps.
