  The Noble Prize in physics 2016 motivates one to study different aspects of
topological properties and topological defects as their related objects.
Considering the significant role of the topological defects (especially
magnetic strings) in cosmology, here, we will investigate three dimensional
horizonless magnetic solutions in the presence of two generalizations: massive
gravity and nonlinear electromagnetic field. The effects of these two
generalizations on properties of the solutions and their geometrical structure
are investigated. The differences between de Sitter and anti de Sitter
solutions are highlighted and conditions regarding the existence of phase
transition in geometrical structure of the solutions are studied.
