The scattering problem for the Schr�dinger equation with a potential linear in time and in space. II. Correctness, smoothness, behavior of the solution at infinity

Whispering Gallery Waves in a Neighborhood of a Higher Order Zero of the Curvature of the Boundary

“…Although we have restricted our study to improving Popov's result, our analysis is a starting point for constructing a local paramatrix which describes the gliding wave generated by an incident wave grazing at an inflection point at the boundary,, Recently, we have noticed that Babich and Smyshlyaev [2] obtained the same result for the special case it-I. However, their method is quite different from ours.…”

Searchlight Asymptotics for High-Frequency Scattering by Boundary Inflection

“…In [4], V.M. Babich and the first author have proved that the solution of (2)-( 5) is in fact classical, using bootstrap-type techniques based on the asymptotic expansion (9), which has allowed to justify (9) with proved error estimates.…”

Thin-layer solutions of the Helmholtz equation

“…in unscaled coordinates (s, n). Also the well posedness of the problem has been proved in [19] and [4]. All this research has strongly suggested that the phase in any superposition of plane waves of the form (1.4) should include a fifth power of λ, as discussed in detail in [10,8].…”

“…in unscaled coordinates (s, n). Also the well-posedness of the problem has been proved in [14] and [13].…”