Oscillon resonances and creation of kinks in particle collisions

We present a numerical study of the process of production of kink-antikink pairs in the collision of particle-like states in the one-dimensional ${\varphi }^4$ model. It is shown that there are 3 steps in the process, the first step is to excite the oscillon intermediate state in the particle collision, the second step is a resonance excitation of the oscillon by the incoming perturbations, and finally, the soliton-antisoliton pair can be created from the resonantly excited oscillon. It is shown that the process depends fractally on the amplitude of the perturbations and the wave number of the perturbation. We also present the effective collective coordinate model for this process.