Hamiltonian approach to isospinning $\mathbb{C}{P}^2$ solitons

Isorotating $\mathbb{C}{P}^2$ Q-solitons in $2+1$ dimensions were studied. Hamiltonian formalism as a more physically meaningful yet fairly demanding approach was adopted during the investigation, which helped to exclude unobservable parameters such as angular frequencies and Lagrangian. This approach also highlighted the non-topological nature of the stabilization mechanism and revealed a number of similarities between well-known $U(1)$ Q-balls and $\mathbb{C}{P}^2$ isospinning solitons, thus rendering the latter a suitable extension of the former for the case of higher Lagrangian symmetry group and paving the way for further $\mathbb{C}{P}^N$ generalizations. Due to the peculiarities of the model, numerical optimisation algorithms were chosen to obtain the solutions.