Abstract
A non-local formulation, depending on a free spectral parameter, is presented governing two ideal fluids separated by a free interface and bounded above either by a free surface or by a rigid lid. This formulation is shown to be related to the Dirichlet–Neumann operators associated with the two-fluid equations. As an application, long wave equations are obtained; these include generalizations of the Benney–Luke and intermediate long wave equations, as well as their higher order perturbations. Computational studies reveal that both equations possess lump-type solutions, which indicate the possible existence of fully localized solitary waves in interfacial fluids with sufficient surface tension.
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