Ondes de gravité stationnaires en profondeur infinie

Gérard Iooss; Pavel Plotnikov; John Toland

doi:10.1016/j.crma.2004.01.002

Ondes de gravité stationnaires en profondeur infinie

Translated title of the contribution: Standing waves on infinite depth

Gérard Iooss, Pavel Plotnikov, John Toland

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

Abstract

The two-dimensional standing wave problem, for an infinitely deep layer, is considered, based on the formulation of the problem as a second order non local PDE. Despite the presence of infinitely many resonances in the linearized problem, we use the Nash-Moser implicit function theorem to prove the existence of standing waves corresponding to values of the amplitude having 0 as a Lebesgue point.

Translated title of the contribution	Standing waves on infinite depth
Original language	French
Pages (from-to)	425-431
Number of pages	7
Journal	Comptes Rendus Mathematique
Volume	338
Issue number	5
DOIs	https://doi.org/10.1016/j.crma.2004.01.002
Publication status	Published - 1 Mar 2004

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2004.01.002

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title = "Ondes de gravit{\'e} stationnaires en profondeur infinie",

abstract = "The two-dimensional standing wave problem, for an infinitely deep layer, is considered, based on the formulation of the problem as a second order non local PDE. Despite the presence of infinitely many resonances in the linearized problem, we use the Nash-Moser implicit function theorem to prove the existence of standing waves corresponding to values of the amplitude having 0 as a Lebesgue point.",

author = "G{\'e}rard Iooss and Pavel Plotnikov and John Toland",

year = "2004",

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doi = "10.1016/j.crma.2004.01.002",

language = "French",

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T1 - Ondes de gravité stationnaires en profondeur infinie

AU - Iooss, Gérard

AU - Plotnikov, Pavel

AU - Toland, John

PY - 2004/3/1

Y1 - 2004/3/1

N2 - The two-dimensional standing wave problem, for an infinitely deep layer, is considered, based on the formulation of the problem as a second order non local PDE. Despite the presence of infinitely many resonances in the linearized problem, we use the Nash-Moser implicit function theorem to prove the existence of standing waves corresponding to values of the amplitude having 0 as a Lebesgue point.

AB - The two-dimensional standing wave problem, for an infinitely deep layer, is considered, based on the formulation of the problem as a second order non local PDE. Despite the presence of infinitely many resonances in the linearized problem, we use the Nash-Moser implicit function theorem to prove the existence of standing waves corresponding to values of the amplitude having 0 as a Lebesgue point.

UR - https://www.scopus.com/pages/publications/1342286313

U2 - 10.1016/j.crma.2004.01.002

DO - 10.1016/j.crma.2004.01.002

M3 - Article

AN - SCOPUS:1342286313

SN - 1631-073X

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SP - 425

EP - 431

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 5

ER -

Ondes de gravité stationnaires en profondeur infinie

Abstract

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