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在研究随机媒质中传播的波的一些有关问题时,常常需要求解波的矩方程。具有不同波数的m-n阶矩方程是一个抛物近似的偏微分波动方程。本文应用格林函数方法将偏微分方程变为积分方程,并用迭代法求得了该积分方程的解。同时,又应用接连散射的方法求解了具有不同波数的m-n阶矩方程,两种方法所得的结果完全相同。文中对解的物理含义作了说明,并讨论了用于波传播研究中的一些问题。
In studying some of the problems associated with waves propagating in random media, it is often necessary to solve the moment equations of the wave. M-n moment equations with different wavenumbers are parabolic approximations of partial differential wave equations. In this paper, the method of Green’s function is used to change the partial differential equation into integral equation, and the solution of the integral equation is obtained by iterative method. At the same time, the method of successive scattering is applied to solve the m-n moment equations with different wavenumbers. The results obtained by the two methods are exactly the same. The physical meaning of solutions is illustrated in this paper, and some problems in wave propagation studies are discussed.