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.

In the first part of this article (after a sketchy theoretical introduction) the various experimental sectors of physics in which Superluminal motions seem to appear are briefly mentioned. In particular, a bird's-eye view is presented of the experiments with evanescent waves (and/or tunneling photons), and with the "localized Superluminal solutions" (SLS) to the wave equation, like the so-called X-shaped beams. In the second part of this paper we present a series of new SLSs to the Maxwell equations, suitable for arbitrary frequencies and arbitrary bandwidths: some of them being endowed with finite total energy. Among the others, we set forth an infinite family of generalizations of the classic X-shaped wave; and show how to deal with the case of a dispersive medium. Results of this kind may find application in other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). This e-print, in large part a review, was prepared for the special issue on "Nontraditional Forms of Light" of the IEEE JSTQE (2003); and a preliminary version of it appeared as Report NSF-ITP-02-93 (ITP, UCSB;2002). Further material can be found in the recent e-prints arVive:0708.1655v2][physics.gen-ph] and arVive:0708.1209v1][physics.gen-ph]. The case of the very interesting (and more orthodox, in a sense) subluminal Localized Waves, solutions to the wave equations, will be dealt with in a coming paper. * It is an old use of ours to write Superluminal with a capital S. † For a more detailed reviews, see P.W.Milonni, in ref.[22] below, and the recent e-prints arVive:0708.1655v2][physics.gen-ph] and arVive:0708.1209v1][physics.gen-ph].

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 a previous paper we showed that localized superluminal solutions to the Maxwell equations exist, which propagate down (nonevanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous nondispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essential role is played by a wave equation (like acoustics, geophysics, etc.).

In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on.

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.