Existence of multimodal standing gravity waves

DOI10.1007/s00021-005-0164-8zbMath1096.76009OpenAlexW1979287215MaRDI QIDQ814403

Gérard Iooss, P. I. Plotnikov

Publication date: 7 February 2006

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-005-0164-8

zbMATH Keywords

bifurcation theorysmall divisor problemstanding gravity wavesNonlinear water waves

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Resonance in context of PDEs (35B34) Abstract bifurcation theory involving nonlinear operators (47J15) Bifurcations in context of PDEs (35B32) Free-surface potential flows for incompressible inviscid fluids (76B07) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (13)

Small divisor problems in fluid mechanics ⋮ KAM for PDEs ⋮ Standing lattice wave patterns of a Boussinesq system ⋮ Traveling water waves — the ebb and flow of two centuries ⋮ On the Fluid Motion in Standing Waves ⋮ Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves ⋮ Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type ⋮ Time quasi-periodic gravity water waves in finite depth ⋮ Quasi-periodic solutions for quasi-linear generalized KdV equations ⋮ Quasi-periodic water waves ⋮ Diamond shaped standing wave patterns of a two-dimensional Boussinesq system ⋮ Standing waves on an infinitely deep perfect fluid under gravity ⋮ Gravity capillary standing water waves

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