Emergence of oscillons in kink-impurity interactions

Abstract

The (1 + 1)-dimensional classical φ 4 theory contains stable, topological excitations in the form of solitary waves or kinks, as well as a non-topological one, 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 structure when introduced as an ansatz in the φ 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.