Non-linear superposition law and Skyrme crystals

TL;DR

This paper presents exact static and time-periodic solutions of the four-dimensional Skyrme model, revealing a nonlinear superposition principle for Skyrmions and discussing their relation to Skyrme crystals.

Contribution

It introduces a nonlinear superposition law for Skyrmions, allowing exact construction of composite solutions and analyzing their interactions.

Findings

Exact static Skyrme configurations with domain wall profiles.

Discovery of a nonlinear superposition principle for Skyrmions.

Exact calculation of interaction energy between Skyrmions.

Abstract

Exact configurations of the four dimensional Skyrme model are presented. The static configurations have the profile which behaves as a kink and, consequently, the corresponding energy momentum tensor describes a domain wall. Furthermore, a class of exact time periodic Skyrmions is discovered. Within such class, it is possible to disclose a remarkable phenomenon which is a genuine effect of the Skyrme term. For a special value of the frequency the Skyrmions admit a non linear superposition principle. One can combine two or more exact elementary Skyrmions (which may depend in a non trivial way on all the space like coordinates) into a new exact composite Skyrmion. Due to such superposition law, despite the explicit presence of non linear effects in the energy momentum tensor, the interaction energy between the elementary Skyrmions can be computed exactly. The relations with the appearance of Skyrme crystals is discussed.