Skyrmion Multi-Walls

TL;DR

This paper numerically investigates multi-wall solutions in the Skyrme system, revealing stable square N-wall configurations that approach the Skyrme crystal, and less stable hexagonal wall solutions.

Contribution

It introduces the existence and stability analysis of parallel multi-wall solutions in the Skyrme model, including the stable square N-wall and less stable hexagonal wall configurations.

Findings

Square N-walls are the most stable multi-wall solutions.

The N→∞ limit of square N-walls approaches the Skyrme crystal.

Parallel hexagonal walls are less stable than square N-walls.

Abstract

Skyrmion walls are topologically-nontrivial solutions of the Skyrme system which are periodic in two spatial directions. We report numerical investigations which show that solutions representing parallel multi-walls exist. The most stable configuration is that of the square $N$-wall, which in the $N\to\infty$ limit becomes the cubically-symmetric Skyrme crystal. There is also a solution resembling parallel hexagonal walls, but this is less stable.