Isospinning $\mathbb{C}{P}^2$ solitons

We study stationary rotating topological solitons in (2+1)-dimensional $\mathbb{C}{P}^2$ non-linear sigma model with a stabilizing potential term. We find families of $U(1)\times U(1)$ symmetric solutions with topological degrees larger than 2, which have two angular frequencies and are labelled by two (one topological and the other non-topological) winding numbers $k_1>k_2$. We discuss properties of these solitons and investigate the domains of their existence.