A note about a new class of two-kinks

We present a model of two-kinks resulting from an explicit composition of two standards kinks of the $phi^4$ model based on the procedure of Ref. cite{uchiyama}. The two-kinks have an additional parameter accounting for the separation of the standard kinks of $phi^4$ model. We have shown that the two-kinks have two discrete internal modes besides the zeroth mode and the continuous spectrum. This new feature signalizes that the head-on collision a two-kinks/two-antikinks pair exhibits a rich and complex behavior due to the additional channel from which the energy of the system can be stored. We have exhibited the fractal structure associated with the main configurations after the collision. We have inferred the fractality as the imprint of the nonlinear exchange of energy into the two discrete internal modes.

The collision of two-kinks defects

We have investigated the head-on collision of a two-kink and a two-antikink pair that arises as a generalization of the $phi^4$ model. We have evolved numerically the Klein-Gordon equation with a new spectral algorithm whose accuracy and convergence were attested by the numerical tests. As a general result, the two-kink pair is annihilated radiating away most of the scalar field. It is possible the production of oscillons-like configurations after the collision that bounce and coalesce to form a small amplitude oscillon at the origin. The new feature is the formation of a sequence of quasi-stationary structures that we have identified as lump-like solutions of non-topological nature. The amount of time these structures survives depends on the fine-tuning of the impact velocity.