  In this paper, the PT -symmetric version of the Maccari system is introduced,
which can be regarded as a two-dimensional generalization of the defocusing
nonlocal nonlinear Schrodinger equation. Various exact solutions of the
nonlocal Maccari system are obtained by means of the Hirota bilinear method,
long-wave limit, and Kadomtsev-Petviashvili (KP) hierarchy method. Bilinear
forms of the nonlocal Maccari system are derived for the first time.
Simultaneously, a new nonlocal Davey-Stewartson-type equation is derived.
Solutions for breathers and breathers on top of periodic line waves are
obtained through the bilinear form of the nonlocal Maccari system. Hyperbolic
line rogue-wave solutions and semi-rational ones, composed of hyperbolic line
rogue wave and periodic line waves are also derived in the long-wave limit. The
semi-rational solutions exhibit a unique dynamical behavior. Additionally,
general line soliton solutions on constant background are generated by
restricting different tau-functions of the KP hierarchy, combined with the
Hirota bilinear method. These solutions exhibit elastic collisions, some of
which have never been reported before in nonlocal systems. Additionally, the
semi-rational solutions, namely (i) fusion of line solitons and lumps into line
solitons, and (ii) fission of line solitons into lumps and line solitons, are
put forward in terms of the KP hierarchy. These novel semi-rational solutions
reduce to 2N-lump solutions of the nonlocal Maccari system with appropriate
parameters. Finally, different characteristics of exact solutions for the
nonlocal Maccari system are summarized. These new results enrich the structure
of waves in nonlocal nonlinear systems, and help to understand new physical
phenomena.
