In this paper, we investigate wave propagation in an inhomogeneous cylindrical waveguide immersed in a medium. To model external medium influence, we use the impedance boundary conditions on the waveguide outer wall. Some structural properties of the dispersion set are studied. To treat the problem of the waveguide forced oscillations, we solve boundary value problems for the first order vector differential equation sequentially in the Fourier transform space and then build the actual space on the basis of the residue theory. The residues for the numerically given function with the first order poles were found by considering auxiliary boundary value problems. The wave fields on the waveguide internal wall are obtained for different inhomogeneity laws and boundary conditions.

中文翻译：

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具有径向不均匀性的浸入式波导中的波传播

在本文中，我们研究了浸入介质中的非均匀圆柱波导中的波传播。为了模拟外部介质的影响，我们使用波导外壁上的阻抗边界条件。研究了色散集的一些结构特性。针对波导受迫振荡问题，我们在傅里叶变换空间中依次求解一阶向量微分方程的边值问题，然后根据残差理论构建实际空间。通过考虑辅助边值问题，找到具有一阶极点的数值给定函数的残差。波导内壁上的波场是针对不同的非均匀性定律和边界条件获得的。