Disclosing the generic behavior of topological solutions through an orbit based approach

Full text: Research into the mathematical properties and physical meaning of topological defects in relativistic field theory has increased sharply since the mid 1970s. For field theories involving two coupled real scalar fields, the mathematical problem concerning the integrability of the equations of motion is much harder, because one deals with two coupled second order nonlinear ordinary differential equations. In this work we present a method, based on the vacuum structure of the potential for system of non-linearly coupled scalar fields in (1 + 1) dimensions, which allows one to get complete information about the behavior of their topological solutions. This is done through an analysis of the orbits connecting the degenerate vacua of the model. The procedure is described by resorting to two examples. In both cases, we analyze the minima of the potential and we also find the BPS and non-BPS sectors. For the BPS sector we find the range of values that the integration constant c0 of the differential orbit equation can assume. In one of the models, c0 has only one critical value, whilst in the other model we have found two critical values for c0. For values of c0 close to the critical ones the BPS solutions for one of the fields present a double-kink profile. Such configurations are typical of first-order phase transition in condensed matter. We notice that such a transition here takes place continuously, without varying any of the parameters of the potential. Instead, it is determined only by the integration constant c0. This should be confronted with other models in the literature which describe first-order phase transition. (author)