Investigation of restricted baby Skyrme models

TL;DR

This paper explores a simplified baby Skyrme model focusing on quartic and potential terms, demonstrating it captures key topological and geometric features of full models, and links soliton properties to multi-skyrmion existence.

Contribution

It provides a detailed analysis of a restricted baby Skyrme model and shows its solutions reflect essential features of the full model, revealing new insights into soliton behavior.

Findings

Restricted model captures topological and geometric features of baby skyrmions.

The nature of solitons in the restricted model correlates with multi-skyrmion existence in the full model.

Compactness of solitons relates to the existence of multi-skyrmions.

Abstract

A restriction of the baby Skyrme model consisting of the quartic and potential terms only is investigated in detail for a wide range of potentials. Further, its properties are compared with those of the corresponding full baby Skyrme models. We find that topological (charge) as well as geometrical (nucleus/shell shape) features of baby skyrmions are captured already by the soliton solutions of the restricted model. Further, we find a coincidence between the compact or non-compact nature of solitons in the restricted model, on the one hand, and the existence or non-existence of multi-skyrmions in the full baby Skyrme model, on the other hand.