Elliptic solutions of the Skyrme model

TL;DR

This paper presents a new class of exact, wave-like solutions to the Skyrme model using elliptic functions, illustrating superpositions of three plane waves, expanding understanding of non-solitonic solutions.

Contribution

It introduces elliptic function-based solutions to the Skyrme model, demonstrating non-solitonic wave solutions and superpositions of plane waves.

Findings

Solutions described by Weierstrass and Jacobi elliptic functions

Solutions are wave-like, not solitonic

Examples of superposition of three plane waves

Abstract

A class of exact solutions of the Skyrme model are obtained. They are described by the Weierstrass $\wp$-function or the Jacobi elliptic function. They are not solitonic but of wave character. They supply us with examples of the superposition of three plane waves in the Skyrme model.