Remarks on the bifurcation of two-dimensional capillary-gravity waves of finite depth
type: Item
instance of: scholarly article
title: Remarks on the bifurcation of two-dimensional capillary-gravity waves of finite depth
zbMATH Open document ID: 0818.76006
author: Hisashi Okamoto
author: Mayumi Shōji
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1995-04-10T00:00:00Z
review text: Summary: We determine two-dimensional water waves of permanent configuration. This problem is a bifurcation problem. We define a mapping \(G\) between two Hilbert spaces and prove that the solutions of the above problem are in one-to-one correspondence to the zeros of the mapping \(G\). Our most important contribution is to clarify the role of the aspect ratio , i.e., the ratio between the mean depth of the flow and the wave length. In particular, we prove that there is no degenerate bifurcation point, whatever the aspect ratio may be.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76B45
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 741435
zbMATH Keywords: double eigenvalue
zbMATH Keywords: mapping
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: aspect ratio
zbMATH Keywords: degenerate bifurcation point
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195165792
OpenAlex ID: W2034099006
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DOI: 10.2977/PRIMS/1195165792
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description: scientific article; zbMATH DE number 741435