Class of exact solutions of the Skyrme and the Faddeev model

TL;DR

This paper presents a new class of exact, wave-like solutions for the Skyrme and Faddeev models, highlighting their superposition of plane waves and unifying their field equations through variable transformation.

Contribution

It introduces a novel class of solutions produced by the interaction of Lagrangian terms, differing from previous solitonic solutions, and demonstrates their wave character.

Findings

Solutions are not solitonic but wave-like.

Field equations of both models can be written in the same form.

Examples of superposition of two plane waves in nonlinear field theories.

Abstract

Class of exact solutions of the Skyrme and the Faddeev model are presented. In contrast to previously found solutions, they are produced by the interplay of the two terms in the Lagrangians of the models. They are not solitonic but of wave character. With an appropriate choice of field variables, the field equations of the two models are written in exactly the same form. The solutions supply us with examples of the superposition of two plane waves in nonlinear field theories.