Potentials of a dissipative waveguide and their application

A singular solution to the two-dimensional dissipative Helmholtz equation in a strip under zero boundary conditions on the walls is considered. The solution, which is constructed by the reflection method, is represented as a series where one term is a fundamental solution to the Helmholtz equation on the plane and the other terms are smooth solutions to the Helmholtz equation in a strip. It is shown that the series formed by smooth solutions is an infinitely differentiable function. Based on the constructed singular solution, the potentials of the single and double layers and the angular potential in a strip are constructed. It is proved that the properties of the strip potentials are determined by the behavior of the well-studied potentials constructed based on the fundamental solution to the Helmholtz equation.