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.

Compensation Process and Generation of Chirped Femtosecond Solitons and Double-kink Solitons in Bose-Einstein Condensates with Time-dependent Atomic Scattering Length in a Time-varying Complex Potential

We consider the one-dimensional (1D) cubic-quintic Gross--Pitaevskii (GP)nequation, which governs the dynamics of Bose--Einstein condensate (BEC) matter waves with time-varying scattering length and loss/gain of atoms in a harmonic trapping potential. We derive the integrability conditions and the compensation condition for the 1D GP equation and obtain, with the help of a cubic-quintic nonlinear Schr\"{o}dinger (NLS) equation with self-steepening and self-frequency shift, exact analytical solitonlike solutions with the corresponding frequency chirp which describe the dynamics of femtosecond solitons and double-kink solitons propagating on a vanishing background. Our investigation shows that under the compensation condition, the matter wave solitons maintain a constant amplitude, the amplitude of the frequency chirp depends on the scattering length, while the motion of both the matter wave solitons and the corresponding chirp depend on the external trapping potential. More interesting, the frequency chirps are localized and their feature depends on the sign of the self-steepening parameter. Our study also shows that our exact solutions can be used to describe the compression of matter wave solitons when the absolute value of the s-wave scattering length increases with time.

Single- and double-kink solutions of a one-dimensional, viscoelastic generalization of Burgers’ equation

Purpose The purpose of this paper is to determine both analytically and numerically the kink solutions to a new one-dimensional, viscoelastic generalization of Burgers’ equation, which includes a non-linear constitutive law, and the number of kinks as functions of the non-linearity and relaxation parameters. Design/methodology/approach An analytical procedure and two explicit finite difference methods based on first-order accurate approximations to the first-order derivatives are used to determine the single- and double-kink solutions. Findings It is shown that only two parameters characterize the solution and that the existence of a shock wave requires that the (semi-positive) relaxation parameter be less than unity and the non-linearity parameter be less than two. It is also shown that negative values of the non-linearity parameter result in kinks with a single inflection point and strain and dissipation rates with a single relative minimum and a single, relative maximum, respectively. For non-linearity parameters between one and two, it is shown that the kink has three inflection points that merge into a single one as this parameter approaches one and that the strain and dissipation rates exhibit relative maxima and minima whose magnitudes decrease and increase as the relaxation and nonlinearity coefficients, respectively, are increased. It is also shown that the viscoelastic generalization of the Burgers equation presented here is related to an ϕ8−scalar field. Originality/value A new, one-dimensional, viscoelastic generalization of Burgers’ equation, which includes a non-linear constitutive law and relaxation is proposed, and its kink solutions are determined both analytically and numerically. The equation and its solutions are connected with scalar field theories and may be used to both studies the effects of the non-linearity and relaxation and assess the accuracy of numerical methods for first-order, non-linear partial differential equations.

Динамические смещения атомов и атермическое скольжение дислокаций в кристаллах

A dislocation glide mechanism at low temperatures is proposed. The mechanism is based on taking into account the dynamic displacements of atoms — displacements caused by nonadiabatic transitions of atoms in a crystal with a dislocation under the action of an external force. Dynamic displacements initiate the instability of a direct dislocation of relatively low-amplitude displacements during atomic vibrations. The development of instability leads to the formation of a double kink and a dislocation shift by one interatomic distance.

Compression of optical similaritons induced by cubic-quintic nonlinear media in a graded-index waveguide

We employ the similarity reductions in two steps to obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrödinger equation. Also, parameter domains are delineated in which kink and double-kink similaritons exist for this model. This methodology introduces a free parameter through cubic nonlinearity coefficient which gives us freedom to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide. Furthermore, we observe rapid beam compression of these similaritons for varying detuning parameter and the coefficient of cubic nonlinearity.

Ultrashort double-kink and algebraic solitons of generalized nonlinear Schrödinger equation in the presence of non-Kerr terms

In this paper, we present bright and dark optical solitons induced by the non-Kerr terms in generalized nonlinear Schrödinger equation. The reported solutions consist of various soliton-like solutions including double-kink and algebraic solitons. These solitons are of sub 10 femtosecond width and are helpful to increase the information carrying capacity in order to make ultrafast communication.