Bags, junctions and networks of BPS and non-BPS defects

We investigate several models of coupled scalar fields that present discrete $Z_2, Z_2\times Z_2$, $Z_3$ 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. We also investigate extended supersymmetric models, which provide concrete examples showing how different the matter fields behave on the background of BPS and non-BPS solutions. 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 how the non-BPS defects of a specific model that engenders the $Z_3$ symmetry may give rise to a stable regular hexagonal network of domain walls