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The theory of internal waves between two bodies of immiscible fluid is important both for its interest to ocean engineering and as a source of numerous interesting mathematical model equations that exhibit nonlinearity and dispersion. In this paper we derive a Hamiltonian formulation of the problem of a dynamic free interface (with rigid lid upper boundary(More)
The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves(More)
The regularized Benjamin–Ono equation appears in the modeling of long-crested interfacial waves in two-fluid systems. For this equation, Fourier–Galerkin and colloca-tion semi-discretizations are proved to be spectrally convergent. A new exact solution is found and used for the experimental validation of the numerical algorithm. The scheme is then used to(More)
This conference aims to bring together researchers working mainly in the mathematical theory of the Nonlinear Dispersive Equations. This class of equations includes but is not restricted to Nonlinear Schrödinger (NLS) equation, Korteweg-de Vries equation, Klein-Gordon equation, Davey-Stewartson system, coupled NLS equations, long wave-short wave resonance(More)
a r t i c l e i n f o a b s t r a c t Keywords: Whitham KdV Modulational instability Fourier–Floquet–Hill method Dispersion Water waves The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation(More)
We derive a new model for the description of large amplitude internal waves in a two-fluid system. The displacement of the interface between the two fluids is assumed to be of small slope, but no smallness assumption is made on the wave amplitude. The derivation of the model is based on the perturbation theory for Hamiltonian systems. In the case of a(More)