In this letter we consider a specific model of braneworld with nonstandard dynamics diffused in the literature, specifically we focus our attention on the matter energy density, the energy of system, the Ricci scalar and the thin brane limit. As the model is classically stable and capable of localize gravity, as a natural extension we address the issue of fermion localization of fermions on a thick brane constructed out from one scalar field with nonstandard kinetic terms coupled with gravity. The contribution of the nonstandard kinetic terms in the problem of fermion localization is analyzed. It is found that the simplest Yukawa coupling ηΨφΨ support the localization of fermions on the thick brane. It is shown that the zero mode for left-handed can be localized on the thick brane depending on the values for the coupling constant η.

In this work we apply point canonical transformations to solve some classes of two coupled nonautonomous nonlinear Schrödinger equations with specific cubic and quintic-time-and space-dependent-nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of nonautonomous nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities.

In this work we present a method, based on the vacuum structure of the potential for a system of two nonlinearly coupled scalar fields in 1 + 1 space-time dimensions, which yields complete information about the behavior of the topological configurations. This is done by means of an analysis of the orbits and the position of the degenerate vacua of the model on the configuration space.

In this work we apply point canonical transformations to solve some classes of nonautonomous, nonlinear Schrödinger equations, namely, those which possess specific cubic and quintic (time-and space-dependent) nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wave function and recover a time-and space-independent nonlinear equation which can be solved explicitly. The method applied here allows us to find wide localized (in space) soliton solutions to the nonautonomous, nonlinear Schrödinger equation. We also generalize the external potential which traps the system and the terms of the nonlinearities.

By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT)-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.