Waves in the Skyrme--Faddeev model and integrable reductions

TL;DR

This paper demonstrates the existence of elliptic function-based nonlinear wave solutions in the Skyrme--Faddeev model and uses Whitham averaging to analyze slow deformations, comparing various integrable reductions.

Contribution

It introduces elliptic function solutions in the Skyrme--Faddeev model and applies Whitham averaging to study their slow modulations, connecting to hydrodynamic reductions.

Findings

Existence of nonlinear wave solutions expressed via elliptic functions.

Application of Whitham averaging to describe slow wave deformation.

Comparison of hydrodynamic reductions with other integrable systems.

Abstract

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation of periodic wave states, leading to a quasi-linear system. The reduction to general hydrodynamic systems have been considered and it is compared with other integrable reductions of the system.