On domain walls in a Ginzburg-Landau non-linear S^2-sigma model

TL;DR

This paper explores the variety and properties of domain wall solutions in a Ginzburg-Landau non-linear $S^2$-sigma model, revealing multiple types of topological and non-topological walls and their mathematical structure.

Contribution

It introduces a detailed classification of domain walls in the model and links their solutions to Hamilton-Jacobi separable trajectories, providing new insights into their structure.

Findings

Identified three basic topological wall types.

Discovered two degenerate families of composite walls.

Linked solutions to Hamilton-Jacobi separable trajectories.

Abstract

The domain wall solutions of a Ginzburg-Landau non-linear $S^2$-sigma hybrid model are unveiled. There are three types of basic topological walls and two types of degenerate families of composite - one topological, the other non-topological- walls. The domain wall solutions are identified as the finite action trajectories (in infinite time) of a related mechanical system that is Hamilton-Jacobi separable in sphero-conical coordinates. The physical and mathematical features of these domain walls are thoroughly discussed.