We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi${}4 model. Our results reveal two different soliton solutions which represent double kink configuration and a kink-nontopological soliton (lump) bound state. Collision of these solitons leads to reveal very rich structure which is related to the reversible energy exchange between the kinks, nontopological solitons and the internal vibrational modes. Various channels of the collisions are discussed; it is shown there is a new type of self-similar fractal structure which appears in the collisions of the relativistic kinks. There the width of the resonance windows increases with the increase of the impact velocity. An analytical approximation scheme is discussed in the limit of the perturbative coupling between the sectors. Considering the spectrum of linear fluctuations around the solitons we found that the double kink configuration is unstable if the coupling constant between the sectors is negative.

We present a numerical study of the process of production of kink-antikink pairs in the collision of particlelike states in the one-dimensional $\phi${}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 number of perturbations. We also present the effective collective coordinate model for this process.

Antikink-kink ($\overline{\mathrm{K}}\mathrm{K}$) collisions in the ${\varphi }^6$ model exhibit resonant scattering although the ${\varphi }^6$ kinks do not support any bound states to which energy could be transferred. In P. Dorey et al. [Kink-Antikink Collisions in the ${\varphi }^6$ Model, Phys. Rev. Lett. 107, 091602 (2011)] it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\overline{\mathrm{K}}\mathrm{K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\overline{\mathrm{K}}\mathrm{K}$ scattering based on this collective bound mode trapped between the $\overline{\mathrm{K}}\mathrm{K}$ pair which allows us to reproduce the full dynamics of $\overline{\mathrm{K}}\mathrm{K}$ scattering with striking accuracy. We also study kink-antikink ($\mathrm{K}\overline{\mathrm{K}}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered.

We consider the Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. The renormalizable Friedberg-Lee-Sirlin model consists of two interacting scalar fields, where the mass of the complex scalar field results from the interaction with the real scalar field which has a finite vacuum expectation value. We here study a new family of self-gravitating axially-symmetric, rotating boson stars in this model. In the flat space limit these boson stars tend to the corresponding Q-balls. Subject to the usual synchronization condition, the model admits spinning hairy black hole solutions with two different types of scalar hair. We here investigate parity-even and parity-odd boson stars and their associated hairy black holes. We explore the domain of existence of the solutions and address some of their physical properties. The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the O(3)-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit.

We study the existence of hairy black holes in the generalized Einstein-Skyrme model. It is proven that in the Bogomol’nyi-Prasad-Sommerfield model limit there are no hairy black hole solutions, although the model admits gravitating (and flat space) solitons. Furthermore, we find strong evidence that a necessary condition for the existence of black holes with Skyrmionic hair is the inclusion of the Skyrme term ${\mathcal{L}}_4$. As an example, we show that there are no hairy black holes in the ${\mathcal{L}}_2+{\mathcal{L}}_6+{\mathcal{L}}_0$ model and present a new kind of black hole solutions with compact Skyrmion hair in the ${\mathcal{L}}_4+{\mathcal{L}}_6+{\mathcal{L}}_0$ model.