  We explore a {\phi}^4 model with an added external parabolic potential term.
This term dramatically alters the spectral properties of the system. We
identify single and multiple kink solutions and examine their stability
features; importantly, all of the stationary structures turn out to be
unstable. We complement these with a dynamical study of the evolution of a
single kink in the trap, as well as of the scattering of kink and anti-kink
solutions of the model. We see that some of the key characteristics of
kink-antikink collisions, such as the critical velocity and the multi-bounce
windows, are sensitively dependent on the trap strength parameter, as well as
the initial displacement of the kink and antikink.
