D. Bazeia

Solitons in systems of coupled scalar fields

Abstract We present a method to obtain soliton solutions to relativistic systems of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential equations that solve the equations of motion when the energy saturates its lower bound. To illustrate the general results, we investigate some systems described by polynomial interactions in the coupled fields.

New global defect structures

We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1. We illustrate the procedure examining specific models and finding explicit solutions.

First-order formalism for bent brane

This work deals with braneworld scenarios in the presence of real scalar field with standard dynamics. We show that the first-order formalism, which exists in the case of flat brane, can be extended to bent brane, for both de Sitter and anti-de Sitter geometry. We illustrate the results with some examples of current interest to high energy physics.

Braneworld models of scalar fields with generalized dynamics

This work deals with braneworld models driven by real scalar fields with nonstandard dynamics. We develop the first-order formalism for models with standard gravity but with the scalar fields having generalized dynamics. We illustrate the results with examples of current interest, and we find analytical and numerical solutions for warp factors and scalar fields. The results indicate that the generalized braneworld scenario is classically stable, and capable of localizing gravity.

First-order formalism and dark energy

This work deals with cosmological models driven by real scalar field, described by standard dynamics in generic spherical, flat, and hyperbolic geometries. We introduce a first-order formalism, which shows how to relate the potential that specifies the scalar field model to Hubbles parameter in a simple and direct manner. Extensions to tachyonic dynamics, and to two or more real scalar fields are also presented.

Solitons with cubic and quintic nonlinearities modulated in space and time.

This work deals with soliton solutions of the nonlinear Schrödinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent paper [J. Belmonte-Beitia, Phys. Rev. Lett. 100, 164102 (2008)], and we solve the equation in the presence of a linear background and cubic and quintic interactions which are modulated in space and time. As a result, we show how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential and the cubic and quintic nonlinearities.

Bags, junctions, and networks of BPS and nonBPS defects

We investigate several models of coupled scalar fields that present discrete

Scalar fields, bent branes, and RG flow

{Z}_{2}{,Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}{,Z}_{3}

Locally localized gravity and geometric transitions

and other symmetries. These models support topological domain wall solutions of the BPS and non-BPS type. The BPS solutions are stable, but the stability of the non-BPS solutions may depend on the parameters that specify the models. The BPS and non-BPS states give rise to bags, and also to three-junctions that may allow the presence of networks of topological defects. In particular, we show that the non-BPS defects of a specific model that engenders the

Generalized global defect solutions

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