Short-wave scattering near the boundary inflection point

DOI10.1007/BF01100149zbMath0621.35034MaRDI QIDQ1089830

Valery P. Smyshlyaev

Publication date: 1987

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

zbMATH Keywords

existenceuniquenessSchrödinger equationsmoothnessinflection pointformal solutionsscattering of short wavesseries of quasi-homogeneous functions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) Series solutions to PDEs (35C10) Schrödinger operator, Schrödinger equation (35J10) Partial differential equations of mathematical physics and other areas of application (35Q99)

Cites Work

• 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
• Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary
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