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Dispersive Nonlinear Waves in Two-Layer Flows with Free Surface Part II. Large Amplitude Solitary Waves Embedded into the Continuous Spectrum

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In this paper we study the dispersive model derived in Part I, for the description of long wave propagation in two-layer flows with free surface. As in the case of the full water–wave problem, this model reproduces the resonance between short waves and long waves. The resulting wave is a generalized solitary wave, characterized by ripples in the far field in addition to the solitary pulse. In this work we focus on particular members of this family resulting from vanishing ripples. These are called embedded solitary waves and they correspond to true homoclinic orbits. Two wave regimes, characterized by elevation or depression of the interface between the layers, are presented. A critical depth ratio separates these two regimes. It is shown how this relates to a change of the global properties for the potential of the Hamiltonian system derived for traveling waves. In oceanic conditions, solitary waves are presented and their broadening is observed as the wave speed increases. We have observed that, for such waves to exist, their speed cannot exceed a certain limit value depending on the density ratio and thickness of each fluid. Finally, other sets of parameters were considered for which multihumped solitons exist, showing the richness and complexity of the Hamiltonian system considered here.
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Document Type: Research Article

Affiliations: Université Aix-Marseille III

Publication date: October 1, 2007

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