Compact Q-balls and Q-shells in a multi-component $\mathbb{C}{P}^N$ model

Coupled multi-component $\mathbb{C}{P}^N$ models with V-shaped potentials are analyzed. It is shown that the model has solutions being combinations of compact Q-balls and Q-shells. The compact nature of solutions permits the existence of novel harbor-type solutions having the form of Q-balls sheltered by Q-shells. The relation between the energy $E$ and Noether charge $Q$ is discussed both analytically and numerically. The energy of the solutions behaves as $E\sim \mathrm{\mid }Q{\mathrm{\mid }}^{\alpha },\alpha <1$, i.e., as for the standard Q-ball. Furthermore, the ratio $E\mathrm{/}Q$ for various configurations in the multi-component model suggests that the solutions are at least classically stable.