Q-balls in the regularized signum-Gordon model

TL;DR

This paper investigates Q-ball solutions in a regularized signum-Gordon model, demonstrating their existence, stability, and convergence to solutions of the unregularized model, with numerical results in three dimensions.

Contribution

It provides the first demonstration of large Q-ball existence and stability in the regularized signum-Gordon model, linking regularized and unregularized solutions.

Findings

Large Q-balls exist for sufficient charge

Large Q-balls are absolutely stable

Regularized solutions approach unregularized solutions

Abstract

The regularized signum-Gordon potential has a smooth minimum and is linear in the modulus of the field value for higher amplitudes. The Q-ball solutions in this model are investigated. Their existence for charges large enough is demonstrated. In three dimensions numerical solutions are presented and the absolute stability of large Q-balls is proved. It is also shown, that the solutions of the regularized model approach uniformly the solution of the unregularized signum-Gordon model. From the stability of Q-balls in the regularized model follows the stability of the solutions in the original theory.