Scattering of plane waves by the junction of transmissive and soft-hard half-planes (Q701760)

The authors study the problem of diffraction of a scalar plane wave by the junction on two half-planes, the transmitting and the soft-hard ones. The velocity potential \(u(x,y)\) satisfies the Helmholtz equation \(\Delta u + k^2 u=0\), \(y\neq 0\) and the boundary conditions on \(y=0\), which are different for \(x<0\) and \(x>0\), namely, the partially transmitting boundary conditions \([u]_-^+ =0\) and \( [\partial u/ \partial y]_-^+ +2ik/\eta u =0\) for \(x<0\) and the soft/hard boundary conditions \(u(x,+0)=0\) and \(\partial u/ \partial y(x,-0)=0\), for \(x>0\). By means of the Fourier transform, the boundary value problem is reduced to a matrix Wiener-Hopf equation. By using the Khrapkov approach, the authors obtain the explicit solution of the factorization problem and show that the uniqueness of the solution is provided by specifying the edge condition (at \(x=0\)). The effect of the ``resistivity'' \(\eta\) on the diffraction is graphically illustrated.