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

DOI10.1007/BF01100135zbMath0621.35076MaRDI QIDQ1089837

Vasilii M. Babich, Valery P. Smyshlyaev

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenesssmoothnessformal asymptoticsshadow zoneinflection pointwhispering gallery wavesboundary flex point

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) Schrödinger operator, Schrödinger equation (35J10)

Related Items (6)

Searchlight asymptotics for high-frequency scattering by boundary inflection ⋮ The Malyuzhinets-Popov diffraction problem revisited ⋮ Contour integral solutions of the parabolic wave equation ⋮ Whispering gallery waves in a neighborhood of a higher order zero of the curvature of the boundary ⋮ Pseudodifferential adiabatic mode parabolic equations in curvilinear coordinates and their numerical solution ⋮ Thin-layer solutions of the Helmholtz equation

Cites Work

• Unnamed Item
• Unnamed Item
• Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I: Asymptotics in the shadow zone
• Direction diagram of radiation in the problem of an inflection point of the boundary
• Whispering-gallery waves in a neighborhood of an inflection point of the boundary. Asymptotics of the wave field as t\(\to \infty\)
• Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary

This page was built for publication: The scattering problem for the Schrödinger equation with a potential linear in time and in space. II: Correctness, smoothness, behavior of the solution at infinity