Topological and non-topological kink families in non-linear [formula omitted]-Sigma models

Abstract

In this paper we construct a family of Hamilton–Jacobi separable non-linear S1×S1 Sigma models for which the kink variety can be analytically identified and for which the linear stability of the emerging kinks is ensured. Furthermore, a model with only one vacuum point is found, where all kinks are forced to be non-topological. The non-simply connectedness of the torus guarantees the global stability of all the non-topological kinks in these models.