First-order formalism for thick branes in $$f(T,{\mathscr {T}})$$ gravity

In this paper we study the thick brane scenario constructed in the recently proposed $$f(T,{\mathscr {T}})$$ f ( T , T ) theories of gravity, where T is called the torsion scalar and $${\mathscr {T}}$$ T is the trace of the energy–momentum tensor. We use the first-order formalism to find analytical solutions for models that include a scalar field as a source. In particular, we describe two interesting case in which in the first we obtain a double-kink solution, which generates a splitting in the brane. In the second case, proper management of a kink solution obtained generates a splitting in the brane intensified by the torsion parameter, evinced by the energy density components satisfying the weak and strong energy conditions. In addition, we investigate the behavior of the gravitational perturbations in this scenario. The parameters that control the torsion and the trace of the energy–momentum tensor tend to shift the massive modes to the core of the brane, keeping a gapless non-localizable and stable tower of massive modes and producing more localized massless modes.

Evidence for the unbinding of the 𝜙4 kink’s shape mode

The 𝜙4 double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is −0.115567λ/M in terms of the coupling λ/4 and the meson mass M evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is −0.433λ/M. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of λ/4 ∼ 0.106M2, where the ℤ2 symmetry is still broken.

A minimal nonlinearity logarithmic potential: Kinks with super-exponential profiles

We study a [Formula: see text]-dimensional field theory based on the [Formula: see text] potential which represents minimal nonlinearity in the context of phase transitions. There are three degenerate minima at [Formula: see text] and [Formula: see text]. There are novel, asymmetric kink solutions of the form [Formula: see text] connecting the minima at [Formula: see text] and [Formula: see text]. The domains with [Formula: see text] repel the linear excitations, the waves (e.g., phonons). Topology restricts the domain sequences and therefore the ordering of the domain walls. Collisions between domain walls are rich for properties such as transmission of kinks and particle conversion, etc. For illustrative purposes we provide a comparison of these results with the [Formula: see text] model and its half-kink solution, which has an exponential tail in contrast to the super-exponential tail for the [Formula: see text] potential. Finally, we place the results in the context of other logarithmic models.

Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation

In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized in all directions in space. Furthermore, the modulation instability is employed to discuss the stability of the available solutions, and the special theorem is also introduced. Moreover, the constraint conditions are also reported which validate the existence of solutions. Furthermore, 2-dimensional graphs are presented for the physical movement of the earned solutions under the appropriate selection of the parameters for stability analysis. The concluded results are helpful for the understanding of the investigation of nonlinear waves and are also vital for numerical and experimental verification in engineering sciences and nonlinear physics.

Kink-type solutions of the SIdV equation and their properties

We study the nonlinear integrable equation, u t + 2(( u x u xx )/ u ) = ϵu xxx , which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen et al. 2012 Commun. Nonlinear Sci. Numer. Simul . 17 , 4115–4124 ( doi:10.1016/j.cnsns.2012.03.001 )). The order- n kink solution u [ n ] of the SIdV equation, which is associated with the n -soliton solution of the Korteweg–de Vries equation, is constructed by using the n -fold Darboux transformation (DT) from zero ‘seed’ solution. The kink-type solutions generated by the onefold, twofold and threefold DT are obtained analytically. The key features of these kink-type solutions are studied, namely their trajectories, phase shifts after collision and decomposition into separate single kink solitons.

Возбуждение волн солитонного типа в кристаллах стехиометрии A-=SUB=-3-=/SUB=-B

In the work, using the molecular dynamics method, the crystals of composition А3В are considered, for example Ni3Al and Pt3Al, for the possibility of excitation of soliton-type waves in them. To describe the interatomic interactions, the potentials obtained by the immersed atom method were used. It is shown that under a harmonic external action, excitation of soliton-type waves is possible in a Pt3Al crystal, but not in Ni3Al. The occurrence of such compression-extension waves is due to the excitation near the zone of action of discrete breathers with a soft type of nonlinearity, the existence of which is impossible in a Ni3Al crystal. The detected waves can propagate thousands of nanometers along a Pt3Al crystal without any loss of shape or speed. The shape of the received wave corresponds to the kink solution of the sin-Gordon equation. The total amount of energy carried by the wave is determined by the number of rows of atoms involved in the oscillations, we can talk about tens and hundreds of electron volts

Является ли кинковое решение нелинейного уравнения Клейна--Гордона солитоном?

The possibility of the existence of soliton solutions of the generalized sine-Gordon equation (also referred to as Kryuchkov-Kukhar equation (KKeq)) has been investigated numerically. This equation describes the propagation of electromagnetic waves in a graphene superlattice. The computational errors associated with the implicit form of the expression defining the kink solution of the considering equation are estimated. The differences between the forms before and after the collision of pulses, propagating towards each other, are estimated. On the basis of the obtained results it is concluded that the considered kink solution is not a soliton.