P. Klimas

Compact gauge K vortices

We investigate a version of the Abelian Higgs model with a non-standard kinetic term (K-field theory) in (2+1) dimensions. The existence of vortex-type solutions with compact support (topological compactons) is established by a combination of analytical and numerical methods. This result demonstrates that the concept of compact solitons in K-field theories can be extended to higher dimensions.

Compact self-gravitating solutions of quartic (K) fields in brane cosmology

Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. First, K field theories allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Second, propagation of linear perturbations is confined inside the compacton domain wall. Further, these linear perturbations inside the topological defect are of the standard type, in spite of the non-standard kinetic term. Third, when gravity is taken into account, location of gravity in the sense of Randall–Sundrum works for these compacton domain walls provided that the backreaction of gravity does not destabilize the compacton domain wall. It is the purpose of the present paper to investigate in detail the existence and stability of compacton domain walls in the full K field and gravity system, using both analytical and numerical methods. We find that the existence of the domain wall in the full system requires a correlation between the gravitational constant and the bulk cosmological constant.

Compact oscillons in the signum-Gordon model

We present explicit solutions of the signum-Gordon scalar field equation which have finite energy and are periodic in time. Such oscillons have strictly finite size. They do not emit radiation.

Quasi-integrable deformations of the SU(3) Affine Toda theory

A bstractWe consider deformations of the SU(3) Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only asymptotically, i.e. in the process of the scattering of two solitons these charges do vary in time, but they return, after the scattering, to the values they had prior to the scattering. This phenomenon, which we have called quasi-integrability, is related to special properties of the two-soliton solutions under space-time parity transformations. Some properties of the AT solitons are discussed, especially those involving interesting static multi-soliton solutions. We support our analytical studies with detailed numerical ones in which the time evolution has been simulated by the 4th order Runge-Kutta method. We find that for some perturbations the solitons repel and for the others they form a quasi-bound state. When we send solitons towards each other they can repel when they come close together with or without ‘flipping’ the fields of the model. The solitons radiate very little and appear to be stable. These results support the ideas of quasi-integrability, i.e. that many effects of integrability also approximately hold for the deformed models.

Compact baby Skyrmions

For the baby Skyrme model with a specific potential, compacton solutions, i.e., configurations with a compact support and parabolic approach to the vacuum, are derived. Specifically, in the nontopological sector, we find spinning Q-balls and Q-shells, as well as peakons. Moreover, we obtain compact baby skyrmions with nontrivial topological charge. All these solutions may form stable multisoliton configurations provided they are sufficiently separated.

Exact vortex solutions in a CPN Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CPN which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x1 + ix2) and x3 + x0 of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

Compact boson stars in K field theories

We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.

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 S3→S3 and suspended Hopf maps, respectively. The Lagrangian of these models is given by a scalar field with a nonstandard kinetic term (K field) coupled to a pure Skyrme term restricted to S2, 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 nontopological compactons of the ball type in 3+1 dimensions are briefly discussed.

Pullback of the volume form, integrable models in higher dimensions and exotic textures

A procedure allowing for the construction of Lorentz invariant integrable models living in d+1 dimensional space time and with an n dimensional target space is provided. Here, integrability is understood as the existence of the generalized zero curvature formulation and infinitely many conserved quantities. A close relation between the Lagrange density of the integrable models and the pullback of the pertinent volume form on target space is established. Moreover, we show that the conserved currents are Noether currents generated by the volume-preserving diffeomorphisms. Further, we show how such models may emerge via Abelian projection of some gauge theories. Then we apply this framework to the construction of integrable models with exotic textures. Particularly, we consider integrable models providing exact suspended Hopf maps, i.e., solitons with a nontrivial topological charge of π4(S3)≅Z2. Finally, some families of integrable models with solitons of πn(Sn) type are constructed. Infinitely many exact s...

Properties of some (3+1)-dimensional vortex solutions of the CP{sup N} model

We construct new classes of vortexlike solutions of the CP{sup N} model in (3+1) dimensions and discuss some of their properties. These solutions are obtained by generalizing to (3+1) dimensions the techniques well established for the two-dimensional CP{sup N} models. We show that as the total energy of these solutions is infinite, they describe evolving vortices and antivortices with the energy density of some configurations varying in time. We also make some further observations about the dynamics of these vortices.