均勻隨機(jī)媒質(zhì)中傳播的波有不同波數(shù)的m-n階矩方程的解
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: 在研究隨機(jī)媒質(zhì)中傳播的波的一些有關(guān)問題時(shí),常常需要求解波的矩方程。具有不同波數(shù)的m-n階矩方程是一個(gè)拋物近似的偏微分波動(dòng)方程。本文應(yīng)用格林函數(shù)方法將偏微分方程變?yōu)榉e分方程,并用迭代法求得了該積分方程的解。同時(shí),又應(yīng)用接連散射的方法求解了具有不同波數(shù)的m-n階矩方程,兩種方法所得的結(jié)果完全相同。文中對解的物理含義作了說明,并討論了用于波傳播研究中的一些問題。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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