In this work we consider kink-antikink collisions for some classes of (1, 1)-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be revealed in a collision process. We consider a particular class of models known as twin theories, where different models lead to same solutions for the equations of motion and same energy density profile. The theories can be distinguished in the level of linear stability of defect structure. We study a class of k-defect theories depending on a parameter M which is the twin theory of the usual φ 4 theory with standard dynamics. For M → ∞ both models are characterized by the same potential. In the regime 1/M 2 << 1, we obtain analytically the spectrum of excitations around the kink solution. It is shown that with the increasing on the parameter 1/M 2 : i) the gap between the zero-mode and the first-excited mode increases and ii) the tendency of one-bounce collision between kink-antikink increases. We numerically investigate kink-antikink scattering, looking for the influence of the parameter changing for the thickness and number of two-bounce windows, and confronting the results with our analytical findings.

We consider a class of topological defects in (1, 1)-dimensions with a deformed φ 4 kink structure whose stability analysis leads to a Schrödinger-like equation with a zeromode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect of the appearance of more than one vibrational mode is the gradual disappearance of the initial two-bounce windows. The total suppression of two-bounce windows even with the presence of a vibrational mode offers a counterexample from what expected from the standard mechanism. For extremely large deformation the defect has a 2-kink structure with one translational and one vibrational mode, and the standard structure of two-bounce windows is recovered.

In this work we examine kink-antikink collisions in two distinct hyperbolic models. The models depend on a deformation parameter, which controls two main characteristics of the potential with two degenerate minima: the height of the barrier and the values of the minima. In particular, the rest mass of the kinks decreases monotonically as the deformation parameter increases, and we identify the appearance of a gradual suppression of two bounce windows in the kink scattering and the production of long lived oscillons. The two effects are reported in connection to the presence of more than one vibrational state in the stability potential. * Electronic address: [1]

In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the φ 6 model. In each topological sector, the potential is symmetric around the local maximum. For φ > 0 there is a linear map between the model and the λφ 4 model. For φ < 0 the potential is reflected. Linear stability analysis of kink and antikink lead to discrete and continuum modes related by a linear coordinate transformation to those known analytically for the λφ 4 model. Fixing one topological sector, the structure of antikinkkink scattering is related to the observed in the λφ 4 model. For kink-antikink collisions a new structure of bounce windows appear. Depending on the initial velocity, one can have oscillations of the scalar field at the center of mass even for one bounce, or a change of topological sector. We also found a structure of one-bounce, with secondary windows corresponding to the changing of the topological sector accumulating close to each one-bounce windows. The kink-kink collisions are characterized by a repulsive interaction and there is no possibility of forming a bound state.

We study the non-integrable φ 6 model on the half-line. The model has two topological sectors.We chose solutions from just one topological sector to fix the initial conditions. The scalar field satisfies a Neumann boundary condition φ x (0, t) = H. We study the scattering of a kink (antikinks) with all possible regular and stable boundaries. When H = 0 the results are the same observed for scattering for the same model in the full line. With the increasing of H, sensible modifications appear in the dynamics with of the defect with several possibilities for the output depending on the initial velocity and the boundary. Our results are confronted with the topological structure and linear stability analysis of kink, antikink and boundary solutions.

In this work we study kink-antikink and antikink-kink collisions in hyperbolic models of fourth and sixth order. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models considered here tend to the polynomial φ 4 and φ 6 models in the limit of small values of the scalar field. We show that kinks and antikinks that interact hyperbolically with fourth order differ sensibly from those governed by the polynomial φ 4 model. The increasing of the order of interaction to the sixth order shows that the hyperbolic and polynomial models give intricate structures of scattering that differ only slightly. The dependence on the order of interaction are related to some characteristics of the models such as the potential of perturbations and the number of vibrational modes.

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In this work we consider kink-antikink and antikink-kink collisions in a modified φ 4 model with a false vacuum characterized by a dimensionless parameter ǫ. The usual φ 4 model is recovered for ǫ = 0. We investigate the ǫ << 1 regime where the kink in the presence of false vacuum can be understood as a small deformation of the standard kink for the φ 4 model. We show that the attractive interaction between the kink-antikink pair leads to a rich scattering pattern, in some cases delaying considerably the false vacuum decay.