  We examine codimension--1 topological defects whose associated worldline is
geodesically embedded in $\AdS_{2}$. This discussion extends a previous study
of exact analytical solutions to the equations of motion of topological defects
in $\AdS_{n}$ in a particular limit where the masses of the scalar and gauge
field vanish. We study the linear perturbations about the zeroth order
kink-like solution and verify that they are stable. We also discuss general
features of the perturbation expansion to all orders.
