Novos métodos analíticos em defeitos topológicos.

Abstract

In this work we study the behavior of a real scalarfield, topological defects and non-topological. Therefore we use the Bogomol’nyi-Prasad-Sommerfield method, which allows us to find the solutions for thee quations of motion of a classical field theory, by using first order differential equations related which the minimal energy of the system. These solutions are called BPS solutions. Here we also review the applicability of the BPS method in a two scalar field theory. More over, we discuss in details the deformation and the extension methods. The extension method which was applied to construct two scalar fields models up to now, is improved to generate new three scalar fields models with analytical solutions. Another key point of this work is the construction a new procedure based on the deformation and the extension methods, in order to generate new analytical models. Such a procedure allowed us to generalize a two scalar fields system involving Lorentz symmetry breaking terms.