Twinlike models for kinks, vortices, and monopoles

This work deals with twinlike models that support topological structures such as kinks, vortices, and monopoles. We investigate the equations of motion and develop the first order framework to show how to build distinct models with the same solution and energy density, as required to make them twinlike models. We also investigate how the stability under small fluctuations behaves and introduce the conditions to get the same stability on general grounds. In particular, we study models that support kinks, vortices, and monopoles in one, two, and three spatial dimensions, respectively.