A two-dimensional soliton system in the Maxwell–Chern–Simons gauge model

The $(2+1)$-dimensional Maxwell–Chern–Simons gauge model consisting of two complex scalar fields interacting through a common Abelian gauge field is considered. It is shown that the model has a solution that describes a soliton system consisting of vortex and Q-ball constituents. This two-dimensional soliton system possesses a quantized magnetic flux and a quantized electric charge. Moreover, the soliton system has a nonzero angular momentum. Properties of this vortex-Q-ball system are investigated by analytical and numerical methods. It is found that the system combines properties of a vortex and a Q-ball.