Solitary Waves in a Two-Layer Fluid with Surface Tension

Abstract

This paper deals with permanent gravity-capillary waves on the interface with surface tension in a two-layer, inviscid, and incompressible fluid between two horizontal, rigid boundaries. It is shown that, if the Bond number $\tau $, a nondimensional surface tension coefficient, is greater thansome critical value $\tau _0$, and the Froude number F is less than, but near some critical value $F_0$, there exists a solitary wave solution which decays to zero at infinity. When $\tau $ is less than $\tau _0$, solitary waves plus a small oscillation at infinity will appear, and the existence of such type of solutions will be investigated in a subsequent paper. Discussions about several critical cases, such as $\tau $ near $\tau _0$ or a density ratio near some critical value, are also given.