Kink excitation spectra in the (1+1)-dimensional φ8\varphi^8 model

We study excitation spectra of BPS-saturated topological solutions -- the kinks -- of the $\varphi^8$ scalar field model in $(1+1)$ dimensions, for three different choices of the model parameters. We demonstrate that some of these kinks have a vibrational mode, apart from the trivial zero (translational) excitation. One of the considered kinks is shown to have three vibrational modes. We perform a numerical calculation of the kink-kink scattering in one of the considered variants of the $\varphi^8$ model, and find the critical collision velocity v_{\scriptsize \mbox{cr}} that separates the different collision regimes: inelastic bounce of the kinks at v_{\scriptsize \mbox{in}}\ge v_{\scriptsize \mbox{cr}}, and capture at v_{\scriptsize \mbox{in}}. We also observe escape windows at some values of v_{\scriptsize \mbox{in}} where the kinks escape to infinity after bouncing off each other two or more times. We analyse the features of these windows and discuss their relation to the resonant energy exchange between the translational and the vibrational excitations of the colliding kinks.Comment: 20 pages, 14 figures; V2: minor changes to match version published in JHE

Scattering of kinks of the sinh-deformed φ4\varphi^4 model

We consider the scattering of kinks of the sinh-deformed $\varphi^4$ model, which is obtained from the well-known $\varphi^4$ model by means of the deformation procedure. Depending on the initial velocity $v_{in}$ of the colliding kinks, different collision scenarios are realized. There is a critical value $v_{cr}$ of the initial velocity, which separates the regime of reflection (at $v_{in}>v_{cr}$) and that of a complicated interaction (at $v_{in}<v_{cr}$) with kinks' capture and escape windows. Besides that, at $v_{in}$ below $v_{cr}$ we observe the formation of a bound state of two oscillons, as well as their escape at some values of $v_{in}$.Comment: 23 pages, 12 figures; v2: minor changes to match version published in EPJ

Classical transitions with the topological number changing in the early Universe

We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the formation and evolution of these solitons, in particular, the conditions at which they could be formed even when the model potential has only one minimum. These non-trivial field configurations represent domain walls in the three-dimensional physical space. The set of these configurations can be split into disjoint equivalence classes. We provide a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the transitions that change the winding number. We also show that non-trivial field configurations could be responsible for the energy density excess that could evade the CMB constraints but could be important at scales which are responsible for the formation of galaxies and the massive primordial black holes.Comment: 17 pages, 5 figures; v3: major revision; matches the published versio

Scalar triplet on a domain wall

We consider a model with a real scalar field with polynomial self-interaction of the fourth degree and a coupled scalar triplet. We demonstrate that there is an exact analytic solution in the form of a domain wall with a localised configuration of the scalar triplet coupled to the wall. We study some properties of this solution.Comment: 4 page

Pendidikan Akhlak Mewujudkan Masyarakat Madani

Islamic education is important role in development and society as a key for continuity in the society. Islamic education in various problem both internally and ekstern required to be able to answer the challenges.There are problems of the value of, as the concept, the credibility gap and idealism.Efforts acceptable solution to this problem is a recipe for the center of islamic education, revitalize education of education and establish a global (International Islamic University) all that is to foster a conducive situation for development of islamic education and goo