A near-BPS analysis for the Skyrme model

The ambition of the project is to describe baryons and nuclei using a particular type of theory, known as the Skyrme model. In this model, the baryons, as well as nuclei, are described by topological solitons in a mesonic field theory. These topological solitons appear as collective excitations of the meson field and, mathematically, they represent solutions of non-linear differential equations. The main aim of the thesis is to study in deep a new type of Skyrme model, known as the "near-BPS Skyrme model". Using this theory, we tried to solve one of the problems of the original Skyrme model, in which the nuclear binding energy was predicted too large. In the thesis, the near-BPS models were studied both in 2 + 1 dimensions and in 3 + 1 dimensions, obtaining new important results.