Domain walls in a non-linear S2$$ {\mathbb{S}}^2 $$-sigma model with homogeneous quartic polynomial potential

A bstractIn this paper the domain wall solutions of a Ginzburg-Landau non-linear S2$$ {\mathbb{S}}^2 $$-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 S2$$ {\mathbb{S}}^2 $$. The stability of all the domain walls is also investigated.