Surface waves on infinite boundaries

Dmitrii Yafaev<sup>ab

a</sup> Université de Rennes , CNRS, IRMAR-UMR 6625, Rennes, France
^b Saint Petersburg State University, Saint Petersburg, Russia

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.

MSC: Primary 47A05, 47A07, 47B25, 47B35; Secondary 47B25, 47B35

Received: 23.12.2024
Revised: 06.03.2025
Accepted: 07.03.2025

DOI: 10.4213/faa4283

 English version: Functional Analysis and Its Applications, 2025, 59:3, 366–389

Bibliographic databases:

• 
• 
•