  In this work, by using the Hirota bilinear method, we obtain one- and
two-soliton solutions of integrable $(2+1)$-dimensional $3$-component Maccari
system which is used as a model describing isolated waves localized in a very
small part of space and related to very well-known systems like nonlinear
Schr\"{o}dinger, Fokas, and long wave resonance systems. We represent all local
and Ablowitz-Musslimani type nonlocal reductions of this system and obtain new
integrable systems. By the help of reduction formulas and soliton solutions of
the $3$-component Maccari system, we obtain one- and two-soliton solutions of
these new integrable local and nonlocal reduced $2$-component Maccari systems.
We also illustrate our solutions by plotting their graphs for particular values
of the parameters.
