Kinks from Dynamical Systems: Domain Walls in a Deformed O(N) Linear Sigma Model

TL;DR

This paper demonstrates how an integrable mechanical system can be used to find all localized static solutions, including kinks, in a deformed O(N) sigma model in two dimensions, revealing a hierarchical structure of solitary waves.

Contribution

It introduces a novel approach using Hamilton-Jacobi separability to classify and analyze kink solutions in a deformed O(N) sigma model.

Findings

All static solutions derived from the integrable system.

Hierarchical structure of solitary wave manifolds for different N.

Explicit characterization of various kink types.

Abstract

It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the mechanical analogue system that follows when time-independent field configurations are being considered. In particular, we describe the properties of the different kinds of kinks in such a way that a hierarchical structure of solitary wave manifolds emerges for distinct N.