Gravity solitary waves with polynomial decay to exponentially small ripples at infinity.

DOI10.1016/S0294-1449(02)00023-9zbMath1068.76008MaRDI QIDQ1400024

Eric Lombardi, Gérard Iooss

Publication date: 30 July 2003

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2003__20_4_669_0

zbMATH Keywords

existenceanalytic continuationoscillatory integralsexponentially small upper bounds

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Solitary waves for incompressible inviscid fluids (76B25) Internal waves for incompressible inviscid fluids (76B55) Soliton equations (35Q51)

Related Items (4)

Numerical computation of solitary waves in a two-layer fluid ⋮ Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples ⋮ Water waves as a spatial dynamical system; infinite depth case ⋮ A variational approach to solitary gravity-capillary interfacial waves with infinite depth

Cites Work

• Unnamed Item
• Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane
• Gravity and capillary-gravity periodic travelling waves for two superposed fluid layers, one being of infinite depth
• Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems. Application to water waves
• Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems
• Exponentially small estimate for the amplitude of capillary ripples of a generalized solitary wave
• Interfacial periodic waves of permanent form with free-surface boundary conditions
• Algebraic Solitary Waves in Stratified Fluids
• Non–existence of truly solitary waves in water with small surface tension
• On the Theory of Internal Waves of Permanent Form in Fluids of Great Depth
• Existence of solitary internal waves in a two-layer fluid of infinite depth
• Gravity travelling waves for two superposed fluid layers, one being of infinite depth: a new type of bifurcation
• Internal waves of permanent form in fluids of great depth
• Solitary internal waves in deep water

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