In this work, the generalized \((3+1)\)-dimensional variable coefficients Kadomtsev–Petviashvili equation, widely used in fluids or plasmas, is analyzed via the unified method and its general form. The multi-soliton rational solutions are obtained including single- and double-soliton rational solutions. Single-soliton shaping and the interactions of double-soliton are graphically discussed in different choices of coefficients. Single-soliton wave keeps its shape, velocity and amplitude unchanged and propagates periodically in a certain direction. The double-soliton waves do not change in shapes, velocities and amplitudes before and after the collisions. We conclude that collisions between the double-soliton waves are elastic and they are not affected by the coefficients of the equation.

在这项工作中，通过统一方法及其一般形式分析了广泛用于流体或等离子体中的广义\（（3 + 1）\）-维变系数Kadomtsev–Petviashvili方程。得到包括单孤子和双孤子有理解的多孤子有理解。在不同的系数选择中以图形方式讨论了单孤子成形和双孤子的相互作用。单孤波保持其形状，速度和振幅不变，并在一定方向上周期性传播。碰撞前后，双孤波的形状，速度和振幅均不变。我们得出结论，双孤波之间的碰撞是弹性的，并且不受方程系数的影响。