To describe the propagation of waves in media containing localized rapidly changing inhomogeneities (e.g., narrow underwater ridges or pycnoclines in the ocean, layers with sharply changing optical or acoustic density, etc.), it is natural to use the wave equation with a small parameter characterizing the ratio of the scales of the localized inhomogeneity and of the general change of velocity (e.g., of the thickness of a pycnocline to the external typical scale of changes in ocean density). We describe the propagation of wave packets whose characteristic wavelength is comparable with the scale of inhomogeneity.

中文翻译：

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具有局部速度摄动的波动方程的短波渐近解

为了描述波在包含局部快速变化的不均匀性（例如，狭窄的水下山脊或海洋中的测斜线，光学或声学密度急剧变化的层等）的介质中的传播，很自然地使用具有小参数的波动方程表征局部不均匀性的尺度与速度的一般变化之比（例如，比索克林的厚度与外部典型的海洋密度变化尺度）。我们描述了特征波长与不均匀性规模相当的波包的传播。