We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects, and we search for explicit defect solutions using the trial orbit method. As we know, under certain circunstances the second order equations of motion can be solved by solutions of first order differential equations. In this case we show that the trial orbit method can be used very efficiently to obtain explicit solutions.In the seventies there appeared a great deal of investigations concerning the presence of topological defects and their role in high energy physics. Particularly interesting issues appeared in the search for defects in models involving real scalar fields, as for instance in the investigations of Refs. [1, 2, 3] which considered models described by two real scalar fields. The interest has been renewed in the nineties, where there has appeared investigations dealing with systems of two scalar field having distinct motivations, as for instance in the case of defects springing in the form of junctions of defects [4,5,6], and also as defects having internal structure [7,8,9]. Other lines of investigations concern the presence of doman walls in supergravity [10,11], in scenarios for localization of gravity on domain walls [12], in supersymmetric gluodynamics, where nonperturbative effects may give rise to gluino condensates [13,14], and also in string theory, since there are models in field theory which correctly describe the low energy world volume dynamics of branes in string theory [15,16,17].A central issue in the investigation of defects in systems involving two real scalar fields concerns integrability of the equations of motion. From the mathematical point of view the problem is hard, because one starts with two coupled second order nonlinear ordinary differential equations -see Refs. [1, 2, 3] for more details. However, in the investigations in Ref.[18] one proposes a new route, in which the mathematical barrier is simplified if one considers a specific class of systems. In this class of systems the equations of motion can be reduced to first order differential equations, which allows obtaining Bogomol'nyi-Prasad-Sommerfield (BPS) states [19,20], which are stable configurations that minimize the energy of the topological solutions.More recently, in Refs. [21,22] one gets two new results, one showing that under certain conditions [21] the second order equations of motion can be reduced to a family of first order equations, in this case ensuring that all the topological solutions are BPS states, and the other showing that sometimes [22] it is possible to find an integrating factor for the first order equations which allows obtaining all the BPS states of the system, thus unveiling the moduli space of topological kinks.As one knows, models described by two real scalar fields are generically described by a Lagrange density, which contains the usual kinetic and gradient contributions, and is otherwise specified by a potential, in general a smooth function of the ...

We investigate the perihelion shift of the planetary motion and the bending of starlight in the Schwarzschild field modified by the presence of a Λ-term plus a conical defect. This analysis generalizes an earlier result obtained by Islam (Phys. Lett. A 97, 239, 1983) to the case of a pure cosmological constant. By using the experimental data we obtain that the parameter ǫ characterizing the conical defect is less than 10 −9 and 10 −7 , respectively, on the length scales associated with such phenomena. In particular, if the defect is generated by a cosmic string, these values correspond to limits on the linear mass densities of 10 19 g/cm and 10 21 g/cm, respectively.

We study quark confinement in a system of two parallel domain walls interpolating different color dielectric media. We use the phenomenological approach in which the confinement of quarks appears considering the QCD vacuum as a color dielectric medium. We explore this phenomenon in QCD2, where the confinement of the color flux between the domain walls manifests, in a scenario where two 0-branes (representing external quark and antiquark) are connected by a QCD string. We obtain solutions of the equations of motion via first-order differential equations. We find a new color confining potential that increases monotonically with the distance between the domain walls.