Topological solitons in scalar field theories in (1+1)-dimensions

Abstract

In this dissertation we study a generalization of the BPS equations, which can be applied in theories with multiplets of scalar fields. We give a overview of the generalized BPS formalism and how it can be applied to the construction of new models from Liealgebras, the FKZ models. We describe the models based on algebras g2 and su(4), and present some static solutions obtained from the BPS equations. Moreover, we also present the results of some simulations for soliton scattering processes in the FKZ model based on algebra su(2).