N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev–Petviashvili equation are derived by means of the Hirota bilinear method, and the limit process of high-order synchronized breathers are shown. Furthermore, M-lump solutions are also presented by taking the long wave limit. Additionally, a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions, their interaction behaviors are shown by three-dimensional plots and contour plots.

中文翻译：

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潜在Kadomtsev–Petviashvili方程的高阶通气，M纠结和半理性解

利用Hirota双线性方法推导了潜在的Kadomtsev–Petviashvili方程的N孤子和高阶同步呼吸解，并给出了高阶同步呼吸的极限过程。此外，还通过考虑长波极限来提出M块解决方案。此外，通过仅对一部分指数函数进行长波限制，生成了具有弹性碰撞的半理性解族，它们的相互作用行为由三维图和轮廓图表示。