Domain walls in a non-linear $\mathbb{S}^2$-sigma model with homogeneous quartic polynomial potential

TL;DR

This paper exactly calculates and analyzes the stability of various domain wall solutions in a non-linear $ ext{S}^2$-sigma model with a quartic potential, using a Bogomolny approach in sphero-conical coordinates.

Contribution

It provides explicit solutions and stability analysis for multiple types of domain walls in a novel non-linear sigma model with a quartic potential.

Findings

Existence of two basic and two composite domain wall solutions.

All domain walls are stable under the studied conditions.

Application of Bogomolny arrangement in sphero-conical coordinates for solution identification.

Abstract

In this paper the domain wall solutions of a Ginzburg-Landau non-linear $\mathbb{S}^2$-sigma hybrid model are exactly calculated. There exist two types of basic domain walls and two families of composite domain walls. The domain wall solutions have been identified by using a Bogomolny arrangement in a system of sphero-conical coordinates on the sphere $\mathbb{S}^2$. The stability of all the domain walls is also investigated.