Moduli spaces and breather dynamics of analytic solutions in Heisenberg exchange-free chiral magnets

TL;DR

This paper explores the moduli spaces and breather dynamics of special analytic solutions in chiral magnets with zero Heisenberg exchange, revealing new families of Skyrmions and breather-like solutions through fluid flow analogies.

Contribution

It introduces a new moduli space of static Skyrmions and identifies infinite-dimensional families of breather-like solutions in a simplified chiral magnet model.

Findings

Discovered a new moduli space of static Skyrmions.

Constructed explicit static and dynamic solutions resembling fluid flow.

Identified infinite-dimensional families of breather-like supercompactons.

Abstract

We investigate the special case of the chiral magnet with vanishing Heisenberg exchange energy, whose axisymmetric Skyrmion solution has previously been found. The dynamical equations of this model look like inviscid fluid flow, and by investigating path lines of this flow we can construct explicit static and dynamic solutions. We find an infinite-dimensional family of static Skyrmions that are related to the axisymmetric Skyrmion by co-ordinate transformations thus discovering a new moduli space, and further infinite-dimensional families of axisymmetric and non-axisymmetric breather-like supercompactons.