Exact solutions for a complex scalar field under discrete symmetry

TL;DR

This paper presents exact solutions for a complex scalar field obeying discrete $Z_N$ symmetry, with implications for integrability, localized structures, and scalar dark matter modeling.

Contribution

It provides the first set of exact solutions for complex scalar fields under discrete symmetry, advancing understanding in integrability and dark matter models.

Findings

Families of exact solutions identified

Potential applications in scalar dark matter modeling

Relevance to integrability and localized structures

Abstract

We report on the presence of families of exact solutions for a complex scalar field that behaves according to the rules of discrete $Z_N$ symmetry. Since the family of models is exactly solved, the results appear to be of interest to integrability, to build junctions and networks of localized structures and to describe scalar dark matter in high energy physics.