Wiener-Hopf vector equations in the diffraction problems on wedges

The mixed boundary value problems for the Helmholtz equation with Dirichlet and Neumann boundary conditions on the parts of the opposite faces are solved. Using the Kontorovich-Lebedev integral transformation the problems are reduced to the modified Wiener-Hopf vector equations that allow factorization and conversion to the equivalent infinite systems of linear second kind algebraic equations. These systems can be solved with pre-specified accuracy for any parameter of the problem and these solutions give the required behavior of the sought function at the demarcation line between the boundary conditions. In the static approximation the analytical form of the solutions are obtained.