On the Theory of Internal Waves of Permanent Form in Fluids of Great Depth

DOI10.2307/2154853zbMath0829.76012OpenAlexW4244929388MaRDI QIDQ4321201

Charles J. Amick

Publication date: 25 January 1996

Full work available at URL: https://doi.org/10.2307/2154853

zbMATH Keywords

hodograph transformationinterfaceDirichlet boundary conditionLaplace equationBenjamin-Ono equationnonlocal nonlinear boundary condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Solitary waves for incompressible inviscid fluids (76B25) Internal waves for incompressible inviscid fluids (76B55) Soliton equations (35Q51) Reaction effects in flows (76V05)

Related Items (9)

Capillary gravity waves on the free surface of an inviscid fluid of infinite depth. Existence of solitary waves ⋮ Gravity solitary waves with polynomial decay to exponentially small ripples at infinity. ⋮ Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane ⋮ Benjamin-Ono periodic bifurcating water waves in presence of an essential spectrum ⋮ Existence of solitary internal waves in a two-layer fluid of infinite depth ⋮ Homoclinic solutions of reversible systems possessing an essential spectrum ⋮ Small-amplitude solitary and generalized solitary traveling waves in a gravity two-layer fluid with vorticity ⋮ Existence, nonexistence, and asymptotics of deep water solitary waves with localized vorticity ⋮ Solitary internal waves in continuously stratified fluids of great depth

Cites Work

• Unnamed Item
• On solitary water-waves of finite amplitude
• Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane
• Small internal waves in two-fluid systems
• Algebraic Solitary Waves in Stratified Fluids
• The stability of internal solitary waves
• A Global Theory of Internal Solitary Waves in Two-Fluid Systems
• On periodic water-waves and their convergence to solitary waves in the long-wave limit
• Elliptic Partial Differential Equations of Second Order
• Uniqueness of Benjamin's Solitary-Wave Solution of the Benjamin-Ono Equation
• Internal waves of permanent form in fluids of great depth
• Solitary internal waves in deep water
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II

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