一、前言 在地下水文学中,常用Boussinesq微分方程来研究有自由面的潜水不稳定运动;近年来由于对水质评价的重视,日益增加研究这类方程的兴趣.不仅如此,广义的Boussi-nesq方程还能描述非饱水土中水分吸收以及非线性介质中热传导等问题.虽然文献[1]用奇异摄动法求得了广义的非线性扩散方程的近似解,但求解过程复杂、计算量大.因此寻找求解过程简单、物理意义清楚的近似解,仍然是有意义的. I. INTRODUCTION In groundwater hydrology, the Boussinesq differential equation is often used to study submersible unsteady motions with free surface. In recent years, due to the emphasis on water quality assessment, interest in such equations has been increasingly studied. Moreover, the generalized Boussi-nesq equation But also the problems of water absorption in non-saturated soils and heat conduction in non-linear media.Although the approximate solution of generalized nonlinear diffusion equation is obtained by singular perturbation in [1], the solution process is complicated and the calculation is large. It is still meaningful to find an approximate solution that has a simple solution process and a clear physical meaning.