  The (1+1)-dimensional classical $\varphi^4$ theory contains stable,
topological excitations in the form of solitary waves or kinks, as well as
stable but non-topological solutions, such as the oscillon. Both are used in
effective descriptions of excitations throughout myriad fields of physics. The
oscillon is well-known to be a coherent, particle-like solution when introduced
as an Ansatz in the $\varphi^4$ theory. Here, we show that oscillons also arise
naturally in the dynamics of the theory, in particular as the result of
kink-antikink collisions in the presence of an impurity. We show that in
addition to the scattering of kinks and the formation of a breather, both bound
oscillon pairs and propagating oscillons may emerge from the collision. We
discuss their resonances and critical velocity as a function of impurity
strength and highlight the role played by the impurity in the scattering
process.
