On the absence of trapped water waves near a cliffed cape

2017/06/01 by Nikolay Kuznetsov, Kuznetsov, Nikolay
Computer Science · Mathematics · #76B15 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1706.00370

openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater than π, whereas the water layer lying under the free surface is of constant depth. Under these assumptions, it is shown that there are no trapped mode solutions of the problem for all values of a non-dimensional spectral parameter; in other words, no point eigenvalues are embedded in the problem's continuous spectrum.

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