In this paper, the -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 -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.

中文翻译：

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对称非局域 Maccari 系统中非零背景上的流氓波和团块

在本文中， 引入了 Maccari 系统的 - 对称版本，它可以看作是散焦非局部非线性薛定谔方程的二维推广。通过 Hirota 双线性方法、长波极限和 Kadomtsev-Petviashvili (KP) 层次方法获得非局部 Maccari 系统的各种精确解。首次推导出非局部 Maccari 系统的双线性形式。同时，导出了一个新的非局部 Davey-Stewartson 型方程。通过非局部 Maccari 系统的双线性形式获得周期线波顶部的呼吸器和呼吸器的解。双曲线流氓波（RW）解和由双曲线RW和周期线波组成的半有理波也在长波极限中推导出来。半有理解表现出独特的动力学行为。此外，通过限制 KP 层次结构的不同 tau 函数，结合 Hirota 双线性方法，可以生成恒定背景下的一般线孤子解。这些解决方案表现出弹性碰撞，其中一些以前从未在非本地系统中报告过。此外，根据KP层次提出了半有理解，即（i）线孤子和团块融合为线孤子和（ii）线孤子裂变为团块和线孤子。这些新的半有理解简化为 其中一些以前从未在非本地系统中报告过。此外，根据KP层次提出了半有理解，即（i）线孤子和团块融合为线孤子和（ii）线孤子裂变为团块和线孤子。这些新的半有理解简化为 其中一些以前从未在非本地系统中报告过。此外，根据KP层次提出了半有理解，即（i）线孤子和团块融合为线孤子和（ii）线孤子裂变为团块和线孤子。这些新的半有理解简化为-具有适当参数的非本地 Maccari 系统的块解。最后总结了非局部Maccari系统精确解的不同特点。这些新结果丰富了非局部非线性系统中波的结构，有助于理解新的物理现象。