Double field domain walls with explicit symmetry breaking

We study the dynamics of domain walls in a double-field model in which the U(1) symmetry is broken both spontaneously and explicitly. The global U(1) symmetry of the system is restored when the symmetry breaking parameter $\epsilon$ is set to zero. Two pairs of degenerate kinks exist in the model with are related to each other by a $Z_2$ transformation. We first calculate the single domain wall solutions and then investigate collision processes. These include simple scattering, pair annihilation, pair capture, and other interesting processes. The possibility of the domain wall being punctured by a string is also investigated.Comment: 15 pages, 7 figure

Fluid Dynamical Description of Sine-Gordon Solitons

We present a fluid dynamical description of a relativistic scalar field in $1+1$ dimensions and apply the general results to the special case of Sine-Gordon solitons. The results which include the local quantities pressure, density and fluid velocity are compared to the standard quantities attributed to the solitons

Dynamics of kink train solutions in deformed Multiple sine-Gordon models

This paper examines the effects of a thin layer of inhomogeneity on periodic solutions of the Multiple-sine-Gordon (MsG) model. We investigate the dynamics of the perturbed Double-sine-Gordon (DsG) system as a significant and more practical case of such configurations. The thin barrier acts as a potential well (potential barrier) and causes critical deformations in kink train solutions and some basic properties of the periodic solutions, such as the type of sub-kinks, their amplitude, energy and wavelength. Stability of the initial kink chain during the interaction with medium defects is analyzed using their phase diagram. Sudden changes in the profile of kink trains due to the disruption of their amplitude and wavelength are considered. The time evolution of moving kink chain solutions while interacting with medium fractures is also studied.Comment: 12 pages, 12 figure

Families of stable and metastable solitons in coupled system of scalar fields

In this paper, we obtain stable and metastable soliton solutions of a coupled system of two real scalar fields with five five discrete points of vacua. These solutions have definite topological charges and rest energies and show classical dynamical stability. From a quantum point of view, however, the V-type solutions are expected to be unstable and decay to D-type solutions. The induced decay of a V-type soliton into two D-type ones is calculated numerically, and shown to be chiral, in the sense that the decay products do not respect left-right symmetry.Comment: 9 pages and 5 figure

Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation

The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter $\epsilon$. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter $\epsilon$ is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.Comment: 17pages, 15 figure

Novel thick brane solutions with

In this work, using two scalar fields ($$\phi$$, $$\psi$$) coupled to 4 + 1 dimensional gravity, we construct novel topological brane solutions through an explicit U(1) symmetry breaking term. The potential of this model is constructed so that two distinct degenerate vacua in the $$\phi$$ field exist, in analogy to the $$\phi ^{4}$$ potential. Therefore, brane solutions appear due to the vacuum structure of the $$\phi$$ field. However, the topology and vacuum structure in the $$\psi$$ direction depends on the symmetry breaking parameter $$\beta ^{2}$$, which leads to different types of branes. As a result, one can interpret the present model as a combination of a $$\phi ^{4}$$ brane with an auxiliary field, which leads to deviations from the $$\phi ^{4}$$ system with the brane achieving a richer internal structure. Furthermore, we analyse in detail the behaviour of the superpotentials, the warp factors, the Ricci and Kretschmann scalars and the Einstein tensor components. In addition to this, we explore the stability of the brane in terms of the free parameters of the model. The analysis presented here complements previous work and is sufficiently novel to be interesting

Soliton models for thick branes

In this work, we present new soliton solutions for thick branes in $$4+1$$ dimensions. In particular, we consider brane models based on the sine-Gordon (SG), $$\varphi ^{4}$$ and $$\varphi ^{6}$$ scalar fields, which have broken $$Z_{2}$$ symmetry in some cases and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacua. These vacua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighborhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the $$w^2$$ term in the expansion of the potential for the resulting Schrödinger-like equation, where w is the five-dimensional coordinate. It turns out that the $$\varphi ^4$$ brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and $$\varphi ^6$$ branes