An extension of Wiener-Hopf method: ordinary differential equationsassociated with diffraction problems

摘要

The problem of plane wave scattering on a strip or on a set ofstrips located in a plane is under consideration. A functional equationof Wiener-Hopf type with analytical restrictions on unknown functions isderived. It is shown that the solution of the problem (the spectrum ofthe scattered field) is a solution of an ordinary differential equation(ODE). The coefficients of the ODE are known up to several constants.The restrictions enabling one to determine the constants are discussed.Thus, the problem of diffraction by strips is reduced to the problem offinding the constants and solving the ODE, but not the integral equation