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

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.