Soliton models for thick branes

In this work, we present new soliton solutions for thick branes in 4+1 dimensions. In particular, we consider brane models based on the sine-Gordon (SG), φ4 and φ6 scalar fields, which have broken Z2 symmetry in some cases and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacua. These vacua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighborhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the w2 term in the expansion of the potential for the resulting Schrödinger-like equation, where w is the five-dimensional coordinate. It turns out that the φ4 brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and φ6 branes.