Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
复制标题
DOI：
10.1093/qjmam/hbad002
复制
发表时间：
2022-11
影响因子：
0.9
通讯作者：
Valentin D. Kunz;R. Assier
中科院分区：
文献类型：
--
作者：
Valentin D. Kunz;R. Assier
本文用双复变量Wiener-Hopf方法研究了直角无衬可穿透楔形体的衍射问题。具体地说，研究了双复变量Wiener-Hopf方程未知（谱）函数的解析性质。我们证明了这些谱函数可以解析地延拓到二维复流形上，并揭示了它们在C2中的奇异性。为此，给出了谱函数的积分表示公式，并得到了充分的应用。结果表明，新的概念添加剂交叉持有穿透楔衍射问题，我们可以重新制定的物理衍射问题作为一个功能的问题，使用这个概念。
We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener–Hopf approach. Specifically, the analyticity properties of the unknown (spectral) functions of the two-complex-variable Wiener–Hopf equation are studied. We show that these spectral functions can be analytically continued onto a two-complex dimensional manifold, and unveil their singularities in C2. To do so, integral representation formulae for the spectral functions are given and thoroughly used. It is shown that the novel concept of additive crossing holds for the penetrable wedge diffraction problem, and that we can reformulate the physical diffraction problem as a functional problem using this concept.