Progress and Prospects in the Theory of Linear Wave Propagation
Progress and Prospects in the Theory of Linear Wave Propagation
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线性波传播理论的进展与展望
DOI：
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发表时间：
1979
期刊：
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通讯作者：
J. Keller
中科院分区：
文献类型：
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作者：
J. Keller
在简要介绍了波的传播之后，描述了线性波传播理论的发展。首先，被认为是经典的技术的图像和分离的变量，其次是索末菲的图像方法的扩展到多片空间，和沃森的变换系列解决方案更迅速收敛的形式。然后介绍了求解某些积分方程的Wiener-Hopf方法和计算散射参数的Schwinger变分法。其次，介绍了传播的简正波理论及其由Pekeris、Fock、Brekhovskikh等人发展起来的理论。然后介绍了WKB方法及其推广。其次是射线理论的讨论，“抛物方程”的方法，和波在非均匀和随机介质。最后展望了未来，重点是使用计算机和计算方法。
The development of the theory of linear wave propagation is described after a brief sketch of what wave propagation is. First the classical techniques of images and separation of variables are considered, followed by Sommerfeld’s extension of the image method to multi-sheeted spaces, and Watson’s transformation of series solutions to more rapidly converging forms. Then the Wiener–Hopf method of solving certain integral equations and Schwinger’s variational method of calculating scattering parameters are introduced. Next the normal mode theory of propagation and its development by Pekeris, Fock, Brekhovskikh and others is described. Then the WKB method and its extensions are presented. This is followed by discussions of ray theory, of the “parabolic equation” method, and of waves in heterogeneous and random media. Finally prospects for the future are considered, with emphasis on the use of computers and methods of calculation.