In this paper, we study a (3+1)-dimensional generalized shallow water wave equation with variable coefficients, which describes the flow below a pressure surface in a fluid. We give the Kadomtsev–Petviashvili hierarchy reduction and construct the multi-soliton solutions and semi-rational solutions in terms of the Gramian. For the multi-soliton solutions, we conclude that: (1) $v_1\left(t\right)$ affects the directions for the two solitons to move; (2) there is the periodic interaction of the two solitons when $v_2\left(t\right)$ is a periodic function and (3) the magnitudes of the velocities for the two solitons increase as the amplitude of the periodic function $v_2\left(t\right)$ increases, where $v_1\left(t\right)$ represents the perturbed effect, $v_2\left(t\right)$ indicates the dispersion effect and t is an independent variable. For the first-order semi-rational solutions, we see that: (1) the fission with $v_1\left(t\right)<0$ and fusion with $v_1\left(t\right)>0$ appear; (2) there is the periodic interaction when $v_2\left(t\right)$ is a periodic function; (3) the magnitude of the velocity for the soliton increases as the amplitude of the periodic function $v_2\left(t\right)$ increases and (4) the lump becomes narrower as the amplitude of the periodic function $v_4\left(t\right)$ decreases, where $v_4\left(t\right)$ indicates the perturbed effect.

在本文中，我们研究了一个（3+1）维广义变系数浅水波动方程，它描述了流体中压力面以下的流动。我们给出了 Kadomtsev-Petviashvili 层次化约简，并根据 Gramian 构造了多孤子解和半有理解。对于多孤子解决方案，我们得出结论：（1）$v_1\left(吨\right)$影响两个孤子移动的方向；(2) 当两个孤子存在周期性相互作用时$v_2\left(吨\right)$是一个周期函数，并且 (3) 两个孤子的速度幅度随着周期函数的幅度而增加$v_2\left(吨\right)$增加，其中$v_1\left(吨\right)$表示扰动效应，$v_2\left(吨\right)$表示分散效应，t是自变量。对于一阶半有理解，我们看到：（1）裂变与$v_1\left(吨\right)<0$并与$v_1\left(吨\right)>0$出现; (2) 存在周期性相互作用时$v_2\left(吨\right)$是周期函数；(3) 孤子的速度幅度随着周期函数幅度的增加而增加$v_2\left(吨\right)$(4) 随着周期函数的幅度增大，团块变窄$v_4\left(吨\right)$减少，其中$v_4\left(吨\right)$表示扰动效应。