Abstract The paper examines the model problem of high-frequency diffraction by a convex surface consisting of two parts. One is soft, the other is hard. The incident wave falls at a small angle to the line which separates soft and hard parts of the surface. The change in the boundary condition provokes the field in the Fock zone to have a rapid transverse variation. This causes a special boundary-layer to be formed. The boundary value problem for the three dimensional parabolic equation is reduced to the Riemann problem solved by the factorization in the form of infinite products containing the zeros of the Airy function and zeros of its derivative. the results of this factorization appear under the sign of double Fourier integral in the representation of the field. Both numerical and asymptotic analysis of this representation is carried out and illustrates the effects of high-frequency diffraction caused by the line of the boundary condition discontinuity.

中文翻译：

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通过将表面软硬部分分开的曲线进行高频纵向衍射

摘要 本文研究了由两部分组成的凸面的高频衍射模型问题。一个是软的，另一个是硬的。入射波与分隔表面软硬部分的线成一个小角度。边界条件的变化引起 Fock 区中的场发生快速的横向变化。这导致形成特殊的边界层。三维抛物线方程的边值问题简化为黎曼问题，通过分解为包含艾里函数零点及其导数零点的无穷积形式进行分解。这种因式分解的结果在场的表示中出现在双傅立叶积分的符号下。