Local and nonlocal $(2+1)$-dimensional Maccari systems and their soliton solutions

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.