  Sine-Gordon kinks are a much studied integrable system that possesses
multi-soliton solutions. Recent studies on sine-Gordon kinks with
space-dependent square-well-type potentials have revealed interesting dynamics
of a single kink interacting with wells and barriers. In this paper, we study a
class of smooth space-dependent potentials and discuss the dynamics of one kink
in the presence of different wells. We also present values for the critical
velocity for different types of barriers. Furthermore, we study two kinks
interacting with various wells and describe interesting trajectories such as
double-trapping, kink knock-out and double-escape.
