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 φ 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 solitonantisoliton 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.
Introduction.Non-linear field theories in the weak coupling regime usually contain two different mass scales associated with the perturbative particle-like states and with the soliton sector of the model, respectively. Conjecture about the role nonperturbative effects, related with the production of the soliton-like states in particle collisions, may play in high energy physics [1], has attracted a lot of attention recently. Over the last two decades the problem of the transition between perturbative and nonperturbative sectors of the theory has been considered in several contexts.Simplest example of the topological solitons in one dimension is the kink solution of the φ 4 model. This model has a number of application in condensed matter physics [2], field theory [3, 4] and cosmology [5]. Dynamical properties of kinks, the processes of their scattering, radiation and annihilation have already been discussed in a number of papers, see e.g. [9][10][11][12][13][14][15][16]. In integrable theories, like the sine-Gordon model, there is no energy loss to radiation and kinks do not annihilate antikinks. However in the non-integrable φ 4 model, the radiation effects in the process of kink-antikink (KK) collision become very important and depending on the impact velocity, the collision may produce various results, e.g., an oscillating bound state can be formed, also the soliton and antisoliton may bounce and reflect from each other.Although the process of annihilation of the KK state of the φ 4 model has been investigated in detail [11,13,16], there is not much information about the inverse process, the creation of the KK pairs by the collision of two identical bunches of particles. In the recent work [6] production KK pair was considered in assumption that two colliding wave trains are composed of the bunches of identical breathers, i.e., tightly coupled KK states. Evidently, the kink-antikink production may proceed even in the case when there is no kink-like states in the initial configuration at all. Here we aim to elucidate the mechanism for this process.In is known that the collision of a kink and an antikink is chaotic, i.e., for some values of the impact velocity the solitons bounce back while for some different impact velocity, smaller or larger, they annihilate [4,16]. This behavior is related with a resonance effect between the
