Mapping properties of normal forms transformations for water waves

DOI10.1007/s40574-016-0078-9zbMath1382.37066OpenAlexW2347087900MaRDI QIDQ295307

Catherine Sulem, Walter Craig

Publication date: 13 June 2016

Published in: Bollettino dell'Unione Matematica Italiana (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40574-016-0078-9

Mathematics Subject Classification ID

Related Items (16)

Quasi-periodic solutions for fractional nonlinear Schrödinger equation ⋮ A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity ⋮ KAM for PDEs ⋮ Recent advances on the global regularity for irrotational water waves ⋮ Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves ⋮ Normal form and dynamics of the Kirchhoff equation ⋮ Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity ⋮ Normal form for the fractional nonlinear Schrödinger equation with cubic nonlinearity ⋮ Quasi-periodic solutions for class of Hamiltonian partial differential equations with fixed constant potential ⋮ The water wave problem and Hamiltonian transformation theory ⋮ On the normal form of the Kirchhoff equation ⋮ On the existence time for the Kirchhoff equation with periodic boundary conditions ⋮ Normal form transformations and Dysthe's equation for the nonlinear modulation of deep-water gravity waves ⋮ Enhanced Existence Time of Solutions to the Fractional Korteweg--de Vries Equation ⋮ Hamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity Waves ⋮ Longer Lifespan for Many Solutions of the Kirchhoff Equation

Cites Work

• On the Cauchy problem for gravity water waves
• Numerical simulation of gravity waves
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Is free-surface hydrodynamics an integrable system?
• A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus
• Normal Form Transformations for Capillary-Gravity Water Waves
• Enhanced Life Span of Smooth Solutions of a Burgers--Hilbert Equation
• Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels
• Sobolev estimates for two dimensional gravity water waves
• Normal forms and quadratic nonlinear Klein-Gordon equations
• Well-posedness of the water-waves equations
• An integrable normal form for water waves in infinite depth
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