In this paper, a new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed. Its integrability is verified by the Painlevé analysis. The bilinear form, multiple-soliton, breather and lump solutions are obtained via using the Hirota bilinear method, a symbolic computation scheme. Furthermore, the abundant dynamical behaviors for these solutions are discovered. It is interesting that there are splitting and fusing phenomena when the lump waves interact. The results can well simulate complex waves and their interaction dynamics in fluids.

中文翻译：

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一个新的（3 + 1）维Kadomtsev–Petviashvili方程及其可积性，多孤子，通气和团波

在本文中，开发了一个新的（3 + 1）维可积Kadomtsev–Petviashvili方程。通过Painlevé分析验证了其可集成性。通过使用Hirota双线性方法（一种符号计算方案），可以得到双线性形式，多孤子，通气和集总解。此外，还发现了这些解决方案的丰富动力学行为。有趣的是，当团块波相互作用时，会出现分裂和融合现象。结果可以很好地模拟复杂的波及其在流体中的相互作用动力学。