  Localised heterogeneities have been recently discovered to act as
bubble-nucleation sites in nonlinear field theories. Vacuum decay seeded by
black holes is one of the most remarkable applications. This article proposes a
simple and exactly solvable $\phi^4$ model exhibiting bubble nucleation around
localised heterogeneities. Bubbles with a rich dynamical behaviour are observed
depending on the topological properties of the heterogeneity. The linear
stability analysis of soliton-bubbles predicts the formation of oscillating
bubbles and the insertion of new bubbles inside an expanding precursor bubble.
Numerical simulations in 2+1 dimensions are in good agreement with theoretical
predictions.
