Rotational symmetry breaking in baby Skyrme models

We consider multisolitons with charges 1 ≤ B ≤ 5 in the baby Skyrme model for the one-parametric family of potentials U = μ² (1 - 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 ≈ 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.