Abstract: Considered in this paper is a two-dimensional rotational two-layered fluid with finite thickness, rigid bottom and upper lid, and acted upon by gravity and interfacial tension. Under the assumption that in both layers of the fluid the horizontal velocity of the fluid particle does not exceed the wave speed, we prove the existence of small-amplitude solitary waves traveling at the interface of the fluid. The argument is mainly based on the center-manifold reduction technique and the dynamical systems methods. By studying the spectrum of the linearization at the equilibrium of the Hamiltonian system formulated from the hydrodynamic problem, and its bifurcation diagram in the parameter plane, we obtain the homoclinic solutions of the reduced system which gives the solitary interfacial water waves.

Key words: Two-layer fluid, Vorticity, Interfacial tension, Bifurcation theory