Class of Exact Solutions of the SU(3) Skyrme Model

TL;DR

This paper extends an ansatz from the SU(2) to the SU(3) Skyrme model, constructing explicit solutions that combine plane waves and elliptic functions, revealing complex rotational structures.

Contribution

It introduces a new class of explicit solutions for the SU(3) Skyrme model using an extended ansatz, highlighting their mathematical structure and physical properties.

Findings

Solutions combine plane waves and Weierstrass elliptic functions.

The solutions describe an asymmetrical top rotating in complex space.

The ansatz is applicable to the SU(3) model, broadening its scope.

Abstract

Recently, Hirayama and Yamashita have presented an ansatz that allows us to construct a class of solutions for the SU(2) Skyrme model. Though these solutions are not solitonic, they provide us with an example on how the plane wave solutions arise in nonlinear field theories. In this paper, we investigate the applicability of the ansatz for the SU(3) Skyrme model. We explicitly construct a class of solutions for the SU(3) model, which in the simplest circumstance is reduced to a combination of the plane waves and Weierstrass elliptic functions. We also discuss some properties of these solutions. For example, the intrinsic structure of these solutions is found to describe an asymmetrical top rotating in the complex three-dimensional space.