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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 Schrödinger 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 (RW) solutions and semirational ones, composed of hyperbolic line RW and periodic line waves are also derived in the long‐wave limit. The semirational 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 semirational 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 semirational 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. [ABSTRACT FROM AUTHOR]

Within the (2 + 1)-dimensional Korteweg–de Vries equation framework, new bilinear Bäcklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function ϕ(y), a family of deformed soliton and deformed breather solutions are presented with the improved Hirota's bilinear method. By choosing the appropriate parameters, their interesting dynamic behaviors are shown in three-dimensional plots. Furthermore, novel rational solutions are generated by taking the limit of the obtained solitons. Additionally, two-dimensional (2D) rogue waves (localized in both space and time) on the soliton plane are presented, we refer to them as deformed 2D rogue waves. The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane, and its evolution process is analyzed in detail. The deformed 2D rogue wave solutions are constructed successfully, which are closely related to the arbitrary function ϕ(y). This new idea is also applicable to other nonlinear systems. [ABSTRACT FROM AUTHOR]

The ( 2 + 1 ) -dimensional [ ( 2 + 1 ) d ] Fokas system is a natural and simple extension of the nonlinear Schrödinger equation (see Eq. (2) in Fokas, 1994). In this letter, we introduce its PT -symmetric version, which is called the ( 2 + 1 ) d nonlocal Fokas system. The N -soliton solutions for this system are obtained by using the Hirota bilinear method whereas the semi-rational solutions are generated by taking the long-wave limit of a part of exponential functions in the general expression of the N -soliton solution. Three kinds of semi-rational solutions, namely (1) a hybrid of rogue waves and periodic line waves, (2) a hybrid of lump and breather solutions, and (3) a hybrid of lump, breather, and periodic line waves are put forward and their rather complicated dynamics is revealed. [ABSTRACT FROM AUTHOR]