Quasi-breathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006). QB's provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB's is worked out in a large class of scalar theories with a general self-interaction potential, in D spatial dimensions. It is shown that the problem of small amplitude QB's is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, Dcrit = 4, above which no small amplitude QB's exist. The QB's obtained this way are shown to provide very good initial data for oscillons. Thus these QB's provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.

The interaction of a kink and a monochromatic plane wave in one dimensional scalar field theories is studied. It is shown that in a large class of models the radiation pressure exerted on the kink is negative, i.e. the kink is pulled towards the source of the radiation. This effect has been observed by numerical simulations in the φ 4 model, and it is explained by a perturbative calculation assuming that the amplitude of the incoming wave is small. Quite importantly the effect is shown to be robust against small perturbations of the φ 4 model. In the sine-Gordon (sG) model the time averaged radiation pressure acting on the kink turns out to be zero. The results of the perturbative computations in the sG model are shown to be in full agreement with an analytical solution corresponding to the superposition of a sG kink with a cnoidal wave. It is also demonstrated that the acceleration of the kink satisfies Newton's law.

A detailed study of vortices is presented in Ginzburg-Landau (or Abelian Higgs) models with two complex scalars (order parameters) assuming a general U(1)×U(1) symmetric potential. Particular emphasis is given to the case, when only one of the scalars obtains a vacuum expectation value (VEV). It is found that for a significantly large domain in parameter space vortices with a scalar field condensate in their core (condensate core, CC) coexist with Abrikosov-Nielsen-Olesen (ANO) vortices. Importantly CC vortices are stable and have lower energy than the ANO ones. Magnetic bags or giant vortices of the order of 1000 flux quanta are favoured to form for the range of parameters ("strong couplings") appearing for the superconducting state of liquid metallic hydrogen (LMH). Furthermore, it is argued that finite energy/unit length 1VEV vortices are smoothly connected to fractional flux 2VEV ones. Stable, finite energy CC-type vortices are also exhibited in the case when one of the scalar fields is neutral.In a considerable number of physical theories describing rather different situations, vortices play often an essential rôle to understand key phenomena. In gauge field theories spontaneously broken by scalar fields, the vortex of reference is undoubtedly the celebrated Abrikosov-NielsenOlesen (ANO) one [1] associated to the breaking of a U(1) gauge symmetry by a complex scalar doublet. ANO vortices correspond to the planar cross-sections of static, straight, magnetic flux-tubes, with an SO(2) cylindrical symmetry. Their magnetic flux is quantized as Φ = nΦ 0 , where Φ 0 is an elementary flux unit and n is an integer. The integer n can be identified with a topological invariant, the winding number of the complex scalar, which is also responsible for their remarkable stability. Rotationally symmetric ANO vortex solutions form families labelled by n and by the mass ratio β = m s /m v , where m s , resp. m v denote the mass of the scalar resp. of the vector field.The ubiquity of vortices in different branches of physics, ranging from condensed matter systems, such as superfluids, superconductors [2,3,4] to cosmic strings in high energy physics [5,6] greatly contributes to their importance. By now models of superconductors with several order parameters (scalar doublets) have become the subject of intense theoretical and experimental studies [7,8]. Under extremely high pressure liquid metallic hydrogen (LMH) is expected to undergo a phase transition to a superconducting state, where two types of Cooper pairs are formed, one from electrons and another one from protons [9,10,11,12,13,14]. For experimental data on the existence of liquid metallic hydrogen see Refs. [15,16], for numerical simulations, 1

Semilocal and electroweak strings are well-known to be unstable against unwinding by the condensation of the second Higgs component in their cores. A large class of current models of dark matter contains dark scalar fields coupled to the Higgs sector of the Standard Model (Higgs portal) and/or dark U(1) gauge fields. It is shown, that Higgsportal-type couplings and a gauge kinetic mixing term of the dark U(1) gauge field have a significant stabilising effect on semilocal strings in the "visible" sector.Cosmic strings and their observational signatures have been studied since a long time as they are expected to form in the early universe [1,2,3,4,5]. Even if by now it seems unlikely that cosmic strings could have significantly contributed to structure formation in the universe, string-like excitations in the Standard Model (SM) continue to be of great interest not only from a theoretical point of view, but such objects may eventually leave observable signatures, e.g., in the Large Hadron Collider [6,7,8]. Remarkable string solutions have been uncovered in the bosonic sector of the Glashow-Salam-Weinberg (GSW) theory (In this paper we shall refer to a generalisation of the electroweak sector of the SM allowing its parameters to take on non-physical values as the GSW theory.), for a review see Ref. [6]. A rather interesting class of models emerges by taking the θ W → π/2 limit of the GSW theory, where θ W denotes the electroweak mixing angle. One obtains this way an Abelian Higgs model with an extended scalar sector having an SU(2) global symmetry acting on the Higgs doublet, this a a prototype of semilocal models. Its strings solutions are referred to as semilocal strings [6,9,10,11] and these are quite instructive to study as being potentially important object in the GSW theory. An important criterion for the physical relevance of string-type objects is their classical stability. Semilocal strings turned out to be stable only when the mass of the scalar particle is smaller than that of the (single) gauge boson, as shown in Refs. [10,11]. The stability of electroweak strings (whose progenitors are the semilocal ones) has been considered in Refs. [6,12,13,14,15]; it was found that for physically realistic values of θ W , electroweak strings are unstable.Moreover there are good reasons to consider extended versions of the GSW theory by a dark sector (DS), motivated by the mystery of dark matter. In such extended models the question of the possible rôle of strings appears naturally. A minimalistic extension of the GSW theory is to couple a (dark) scalar field to the by now firmly established Higgs sector of the GSW theory (Higgs portal) [16,17], but there are also well motivated extensions of the 1 GSW theory containing U(1) gauge fields in the DS [18,19]. In Refs. [20,21,22,23,24,25] physical properties and possible observational signatures of cosmic strings in the DS (dark strings) have been considered. A more detailed investigation of string solutions in Abelian Higgs theories modelling a "visible" and a "...

In a class of two-component Ginzburg-Landau models (TCGL) with a U(1)×U(1) symmetric potential, vortices with a condensate at their core may have significantly lower energies than the Abrikosov-Nielsen-Olesen (ANO) ones. On the example of liquid metallic hydrogen (LMH) above the critical temperature for protons we show that the ANO vortices become unstable against core-condensation, while condensate-core (CC) vortices are stable. For LMH the ratio of the masses of the two types of condensates, M = m 2 /m 1 is large, and then as a consequence the energy per flux quantum of the vortices, E n /n becomes a non-monotonous function of the number of flux quanta, n. This leads to yet another manifestation of neither type 1 nor type 2, (type 1.5) superconductivity: superconducting and normal domains coexist while various "giant" vortices form. We note that LMH provides a particularly clean example of type 1.5 state as the interband coupling between electronic and protonic Cooper-pairs is forbidden.