We develop an approach to writing efficient short-wave asymptotics based on the representation of the Maslov canonical operator in a neighborhood of generic caustics in the form of special functions of a composite argument. A constructive method is proposed that allows expressing the canonical operator near a caustic cusp corresponding to the Lagrangian singularity of type \(A_3\) (standard cusp) in terms of the Pearcey function and its first derivatives. It is shown that, conversely, the representation of a Pearcey type integral via the canonical operator turns out to be a very simple way to obtain its asymptotics for large real values of the arguments in terms of Airy functions and WKB-type functions.

中文翻译：

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拉格朗日流形和腐蚀性尖峰附近的有效短波渐近线

我们开发了一种有效的短波渐近线的编写方法，该方法基于复合论元的特殊函数形式的通用焦散附近的Maslov规范运算符的表示。提出了一种构造方法，该方法允许根据皮尔西函数及其一阶导数在对应于\（A_3 \）类型的拉格朗日奇点的苛性尖点附近表达规范算子（标准尖点）。相反，证明了通过规范运算符表示Pearcey型积分是一种非常简单的方法，可以从Airy函数和WKB型函数的参数的大实数值中获得其渐近性。