Multimodal standing gravity waves: a completely resonant system

DOI10.1007/s00021-004-0128-4zbMath1065.35051OpenAlexW2044804058MaRDI QIDQ1773126

P. I. Plotnikov, Gérard Iooss

Publication date: 25 April 2005

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

Full work available at URL: https://hal.univ-cotedazur.fr/hal-01265187/file/GI-PP_1.pdf

zbMATH Keywords

nonlinear water wavesformal solutionsnonlocal PDEinfinite dimensional bifurcation equationdoubly 2\(\pi\)-periodic solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Periodic solutions to PDEs (35B10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Asymptotic expansions of solutions to PDEs (35C20) Resonance in context of PDEs (35B34) Bifurcations in context of PDEs (35B32) Free-surface potential flows for incompressible inviscid fluids (76B07) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)

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