A generalized Burgers equation with variable coefficients is introduced based on the (2+1)-dimensional Burgers equation. Using the test function method combined with the bilinear form, we obtain the lump solutions to the generalized Burgers equation with variable coefficients. The amplitude and velocity of the extremum point are derived to analyze the propagation of the lump wave. Moreover, we derive and study the mixed solutions including lump-one-kink and lump-two-kink cases. With symbolic computation, two cases of relations among the parameters are yielded corresponding to the solutions. Different and interesting interaction phenomena arise from assigning abundant functions to the variable coefficients. Especially, we find that the shape of kink waves might be parabolic type, and one lump wave can be decomposed into two lump waves. The test function method is applicable for the generalized Burgers equation with variable coefficients, and it will be applied to some other variable-coefficient equations in the future.

基于（2 + 1）维Burgers方程，引入了一个变系数广义Burgers方程。使用检验函数方法和双线性形式，我们得到了变系数广义伯格斯方程的总解。推导了极值点的幅度和速度，以分析团波的传播。此外，我们推导并研究了混合解决方案，包括一次总付和两次总付。通过符号计算，对应于解产生了参数之间的关系的两种情况。为变量系数分配丰富的函数会产生不同而有趣的相互作用现象。特别是，我们发现扭结波的形状可能是抛物线型的，并且一个团块波可以分解为两个团块波。