Semiclassical asymptotics for a radial Schrödinger equation with singular potential

For a radial Schrödinger equation with singular potential, the semiclassical asymptotic behavior corresponding to noncompact Lagrangian manifolds is obtained.Institute of Problems of Mechanics, Russian Academy of Sciences; CINVESTAV del IPN, Mexico. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 56–59, January, 1994.     

On the convergence of the amplitude of the diffracted nonstationary wave in scattering by wedges

We make more precise the Limiting Amplitude Principle in the two-dimensional scattering of an incident plane harmonic wave by a wedge. We find the long-time asymptotic regime of convergence of the amplitude of the cylindrical wave diffracted by the vertex of a wedge to the limiting amplitude of the solution to the corresponding stationary problem. The asymptotics turns out to be uniform on compacta and depends on the magnitude of the wedge and the profile of the incident wave. The cases of Dirichlet-Dirichlet and Dirichlet-Neumann boundary conditions are considered.     

Asymptotic fast-decreasing solutions of linear,strictly hyperbolic systems with variable coefficients

Translated from Matematicheskie Zametki, Vol. 49, No. 4, pp. 31–46, April, 1991.