Communicated by M. CostabelWe continue our study of a nonstationary scattering by wedges. In this paper we consider nonstationary scattering of plane waves by a 'hard-soft' wedge. We prove the uniqueness and existence of a solution to the corresponding DN-Cauchy problem in appropriate functional spaces. We also give the explicit form of the solution and prove the Limiting Amplitude Principle.

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Communicated by V. V. KravchenkoWe obtain explicit formulas for the scattering of plane waves with arbitrary profile by a wedge under Dirichlet, Neumann and Dirichlet-Neumann boundary conditions. The diffracted wave is given by a convolution of the profile function with a suitable kernel corresponding to the boundary conditions. We prove the existence and uniqueness of solutions in appropriate classes of distributions and establish the Sommerfeld type representation for the diffracted wave. As an application, we establish (i) stability of long-time asymptotic local perturbations of the profile functions and (ii) the limiting amplitude principle in the case of a harmonic incident wave. 4774-4785 O u. y, !/ is the Fourier-Laplace transform of a distribution u 2 S 0 .Q I R C /. Definition A.2We denote by HP.C C , S 0 .Q// the space of holomorphic functions in C C with values in S 0 .Q/ satisfying bound (A2) for some m, N 2 I N.

On the other hand, the uniqueness in the Keller-Blank approach was not studied before. Our result means that the Keller-Blank solution belongs to our functional classes. We prove the coincidence for DD and NN-boundary conditions. Moreover, we obtain the solution for the DN-case.

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.