The problem of waves in an inhomogeneous cylindrical waveguide with an annular crack is considered. A system of integral equations with hypersingular kernels is obtained for finding jumps in radial and longitudinal displacements on the sides of a crack. For the solution, a scheme based on the boundary element method was used. An asymptotic solution to the system of integral equations is constructed for when the defect width tends to zero. The results of computational experiments on comparing solutions obtained by two methods are presented.

中文翻译：

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有限宽度环形裂纹的非均匀波导振荡问题的数值和渐近解

考虑了具有环形裂纹的不均匀圆柱波导中的波问题。获得具有超奇异核的积分方程组，以查找裂纹侧面的径向和纵向位移的跳跃。对于该解决方案，使用了基于边界元方法的方案。当缺陷宽度趋于零时，构造积分方程系统的渐近解。给出了比较两种方法获得的解的计算实验结果。