Rotational symmetry breaking in baby Skyrme models

TL;DR

This paper investigates how rotational symmetry in baby Skyrme models with various potentials is preserved or broken for multisolitons with charges 1 to 5, revealing critical potential parameters affecting symmetry and stability.

Contribution

It introduces a generalized family of baby Skyrme models with variable potentials and analyzes the symmetry and stability of multisolitons across different charges and potential parameters.

Findings

Stable charge-one solutions are always rotationally symmetric.

Higher charges lose symmetry above a critical potential parameter s.

Spatial energy distributions reveal symmetry breaking and soliton interactions.

Abstract

We consider multisolitons with charges 1 =< B =< 5 in the baby Skyrme model for the one-parametric family of potentials U=\mu^2 (1-\phi_3)^s with 0<s =< 4. This class of potentials is a generalization of the `old' (s=1) and `holomorphic' (s=4) baby Skyrme models. We find that for charge one, stable solutions exist for every value of s and they are rotationally-symmetric. For higher charges, stable solutions exist only below s \approx 2. In the charge-two sector the stable solutions are always rotationally-symmetric and ring-like. For charge three and above, rotational symmetry is exhibited only in the small s region; above a certain critical value of s, this symmetry is broken and a strong repulsion between the constituent one-Skyrmions becomes apparent. We also compute the spatial energy distributions of these solutions.