Abstract
A solitary wave with an oscillatory tail at infinity, the so-called generalized solitary wave, is a new phenomenon only discovered recently due to the presence of small surface tension on the free surface of a liquid layer of constant density under gravity. The purpose of this paper is to show that the effect of density variation alone can also cause generalized solitary waves. The problem under consideration deals with a two-layer liquid under gravity bounded below by a rigid horizontal bottom and above by a free surface in the absence of surface tension. An exact theory is developed for the existence of a generalized solitary wave as an internal wave in the two-layer liquid.
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