  We study various properties of a perturbed signum-Gordon model, which has
been obtained through the dimensional reduction of the called `first BPS
submodel of the Skyrme model'. This study is motivated by the observation that
the first BPS submodel of the Skyrme model may be partially responsible for the
good qualities of the rational map ansatz approximation to the solutions of the
Skyrme model. We investigate the existence, stability and various properties of
oscillons and other time-dependent states in this perturbed signum-Gordon
model.
