Under investigation in this paper is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota–Riemann method. Magnitude and velocity of the one soliton are derived. Graphs are presented to discuss the solitons and one-periodic waves: the coefficients in the equation can determine the velocity components of the one soliton, but cannot alter the soliton magnitude; the interaction between the two solitons is elastic; the coefficients in the equation can influence the periods and velocities of the periodic waves. Relation between the one-soliton solution and one-periodic wave solution is investigated.

本文研究的是流体动力学和等离子体物理学中的广义 (3+1) 维 Kadomtsev-Petviashvili 方程。孤子解和单周期波解是通过 Hirota 双线性方法和 Hirota-Riemann 方法获得的。推导出一个孤子的大小和速度。用图表讨论孤子和单周期波：方程中的系数可以确定一个孤子的速度分量，但不能改变孤子的大小；两个孤子之间的相互作用是弹性的；方程中的系数会影响周期波的周期和速度。研究了单孤子解和一周期波解之间的关系。