Abstract
Long periodic waves propagating in a channel bounded above and below by horizontal walls are considered. The fluid consists of two layers of constant densities separated by a region in which the density varies continuously. The problem is solved numerically by a finite difference scheme coupled with boundary integral equation techniques. It is shown that there are long periodic waves characterized by a train of ripples in their troughs. The numerical results suggest the existence of a wave with one large crest flanked on either side by a small-amplitude oscillatory wave extending to infinity, in anology with the ‘‘solitary wave with oscillatory tail,’’ known to exist for surface waves with small surface tension.
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