均匀随机媒质中传播的波有不同波数的m-n阶矩方程的解
THE WAVE PROPAGATION IN A HOMOGENEOUS RANDOM MEDIUMTHE SOLUTION OF THE m-nth MOMENT EQUATION WITH DIFFERENT WAVE NUMBERS
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摘要: 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。Abstract: In the study of the problems related to the wave propagation in random media, the solutions of the moment equations are often needed. The m-nth moment equation with different wave numbers is a differential equation. In the present paper, the author converts the parabolic differental equation to an integral equation by using the Green s functions. The solution of the moment equation is got by using the iteration method. The solution of the moment equation is also got by using the method of successive scattering. It is shown that the solution by two different mehtods are identical. The physical implication of the successive solution of the m-nth moment equation is explained. Some of the applications of the solutions of the mement equations are discussed briefly.
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