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

The problem of plane wave scattering on a strip or on a set of strips located in a plane is under consideration. A functional equation of Wiener-Hopf type with analytical restrictions on unknown functions is derived. It is shown that the solution of the problem (the spectrum of the 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 of finding the constants and solving the ODE, but not the integral equation.