Compact shell solitons in K field theories

Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological solitons, and may be classified as maps $S^3 \to S^3$ and suspended Hopf maps, respectively. The Lagrangian of these models is given by a scalar field with a non-standard kinetic term (K field) coupled to a pure Skyrme term restricted to $S^2$, rised to the appropriate power to avoid the Derrick scaling argument. Further, the existence of infinitely many exact shell solitons is explained using the generalized integrability approach. Finally, similar models allowing for non-topological compactons of the ball type in 3+1 dimensions are briefly discussed.Comment: 10 pages, latex, 2 figures, change in title and introduction. Discussion section, 2 figures and references adde

Some Comments on BPS systems

We look at simple BPS systems involving more than one field. We discuss the conditions that have to be imposed on various terms in Lagrangians involving many fields to produce BPS systems and then look in more detail at the simplest of such cases. We analyse in detail BPS systems involving 2 interacting Sine-Gordon like fields, both when one of them has a kink solution and the second one either a kink or an antikink solution. We take their solitonic static solutions and use them as initial conditions for their evolution in Lorentz covariant versions of such models. We send these structures towards themselves and find that when they interact weakly they can pass through each other with a phase shift which is related to the strength of their interaction. When they interact strongly they repel and reflect on each other. We use the method of a modified gradient flow in order to visualize the solutions in the space of fields.Comment: 27 pages, 17 figure

Scattering of compact kinks

We study the scattering processes of kink-antikink and kink-kink pairs in a field theory model with non-differentiable potential at its minima. The kink-antikink scattering includes cases of capture and escape of the soliton pair separated by a critical velocity, without windows of multi bounce followed by escape. Around the critical velocity, the behavior is fractal. The emission of radiation strongly influences the small velocity cases, with the most radiative cases being also the most chaotic. The radiation appears through the emission of compact oscillons and the formation of compact shockwaves. The kink-kink scattering happens elastically, with no emission of radiation. Some features of both the kink-antikink and the kink-kink scattering are explained using a collective coordinate model, even though the kink-kink case exhibits a null-vector problem.Comment: 22 pages, 14 figure

Scaling, self-similar solutions and shock waves for V-shaped field potentials

We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential $V(\phi)| = |\phi|.$ It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with infinite number of degrees of freedom. The model has an interesting scaling symmetry of the 'on shell' type. We find self-similar as well as shock wave solutions of the field equation in that model.Comment: Two comments and one reference adde