The (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied in this paper by constructing the Hirota bilinear form. The lump solution of the equation is obtained by bilinear form, and the conditions for the existence of the solution are obtained. The picture description of lump solution is further given. On the other hand, we also give the collision phenomena of lump solution, periodic wave solution and a single-kink soliton solution when the (3+1)-dimensional KP equation reduces to z = y and z = t by means of the Hirota method. The collision phenomenon is shown in the 3D plot description, the dynamic characteristics of the collision are also analyzed.

中文翻译：

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具有集中解的(3+1)维KP方程及其碰撞现象研究

本文通过构建 Hirota 双线性形式来研究 (3+1) 维 Kadomtsev-Petviashvili (KP) 方程。用双线性形式得到方程的集中解，得到解存在的条件。进一步给出了块状溶液的图片描述。另一方面，我们也给出了当（3+1）维KP方程简化为z = 是的和z = 吨通过广田方法。碰撞现象显示在3D绘图描述中，还分析了碰撞的动态特性。