  Nonlinear wave propagation plays a crucial role in the functioning of many
physical and biophysical systems. In the propagation regime, disturbances due
to the presence of local external perturbations, such as localised defects or
boundary interphase walls have gained great attention. In this article, the
complex phenomena that occur when sine-Gordon line solitons collide with
localised inhomogeneities are investigated. By a one-dimensional theory, it is
shown that internal modes of two-dimensional sine-Gordon solitons can be
activated depending on the topological properties of the inhomogeneities. Shape
mode instabilities cause the formation of bubble-like and drop-like structures
for both stationary and travelling line solitons. It is shown that such
structures are formed and stabilised by arrays of localised inhomogeneities
distributed in space. Implications of the observed phenomena in physical and
biological systems are discussed.
