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Funktsional'nyi Analiz i ego Prilozheniya, 2025, Volume 59, Issue 3, Pages 185–215
DOI: https://doi.org/10.4213/faa4283 (Mi faa4283) 		 
Surface waves on infinite boundaries

Dmitrii Yafaevab

a Université de Rennes , CNRS, IRMAR-UMR 6625, Rennes, France
b Saint Petersburg State University, Saint Petersburg, Russia
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DOI: https://doi.org/10.4213/faa4283
Abstract: We develop scattering theory for the Laplace operator in the half-space with Robin type boundary conditions on the boundary plane. In particular, we show that, in addition to usual space waves living in cones and described by standard wave operators, surface waves may arise in this problem. They are localized in parabolic neighbourhoods of the boundary. We find conditions on the boundary coefficient ensuring the existence of surface waves. Several open problems are formulated.
Keywords: Schrödinger equation, asymptotics at infinity, surface waves.
Received: 23.12.2024
Revised: 06.03.2025
Accepted: 07.03.2025
Published: 11.08.2025
English version:
Functional Analysis and Its Applications, 2025, Volume 59, Issue 3, Pages 366–389
DOI: https://doi.org/10.1134/S1234567825030115
Bibliographic databases:
Document Type: Article
MSC: Primary 47A05, 47A07, 47B25, 47B35; Secondary 47B25, 47B35
Language: Russian
Citation: Dmitrii Yafaev, “Surface waves on infinite boundaries”, Funktsional. Anal. i Prilozhen., 59:3 (2025), 185–215; Funct. Anal. Appl., 59:3 (2025), 366–389
Citation in format AMSBIB
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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