ABSTRACT

The propagation of a wave from a point source when the velocity \(v\) in the medium is expressed as \(v = \frac {1}{\sqrt y}\) is considered. Exact solutions to the corresponding eikonal equation are obtained and numerically verified. It is shown that the solution of this equation when the point source is at the origin of coordinates is not unique.

中文翻译：

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二维Eikonal方程的一族解

摘要

当介质中的速度\（v \） 表示为\（v = \ frac {1} {\ sqrt y} \）时 ，考虑了从点源传播的波 。获得了相应的方程方程的精确解并进行了数值验证。结果表明，当点源位于坐标原点时，该方程的解不是唯一的。