Gauged compact $Q$-balls and $Q$-shells in a multi-component $CP^N$ model

We study a multicomponent $CP^N$ model's scalar electrodynamics. The model contains $Q$-balls and $Q$-shells, which are nontopological compact solitons with time dependency $e^{i\omega t}$. Two coupled $CP^N$ models can decouple locally if one of their $CP^N$ fields takes the vacuum value. Because of the compacton nature of solutions, $Q$-shells can shelter another compact $Q$-ball or $Q$-shell within their hollow region. Even if compactons do not overlap, they can interact through the electromagnetic field. We investigate how the size of multicompacton formations is affected by electric charge, with a focus on structures with nonzero or zero total net charge.