Emergence of oscillons in kink-impurity interactions

The (1+1)-dimensional classical ${\phi }^4$ 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 ${\phi }^4$ 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.