Domain wall solution of the Skyrme model

TL;DR

This paper analytically derives a class of domain-wall solutions in the Skyrme model, characterized by hyperbolic tangent functions, revealing their energy density behavior and connection to Weierstrass functions.

Contribution

It introduces a new class of analytical domain-wall solutions in the Skyrme model using hyperbolic tangent functions as a special limit of Weierstrass functions.

Findings

Solutions exhibit domain-wall-like energy density profiles.

One energy term behaves like a domain wall, the other becomes constant at large distances.

Analytical solutions are expressed via tangent hyperbolic functions.

Abstract

A class of domain-wall-like solutions of the Skyrme model is obtained analytically. They are described by the tangent hyperbolic function, which is a special limit of the Weierstrass $\wp$ function. The behavior of one of the two terms in the static energy density is like that of a domain wall. The other term in the static energy density does not vanish but becomes constant at the points far apart from the wall.