Small-amplitude Solitary Interfacial Traveling Waves In A Gravity-capillary Two-layered Fluid With Vorticity

This thesis proves existence of small-amplitude solitary interfacial traveling waves on a two-dimensional rotational two-layer fluid.It is assumed that the fluid admits finite thickness,rigid bottom and upper lid,and is acted upon by gravity and interfacial tension.In addition,we assume that there are no relative stationary points in the fluid,which means that the wave velocity is greater than the horizontal velocity of particles in two layers of the fluid.The argument is mainly based on the center-manifold reduction technique and the dynamical systems methods.Considering the horizontal spatial direction as a timelike variable,the hydrodynamic problem is formulated as an infinite dimensional Hamiltonian system.A center-manifold reduction technique is applied to reduce the hydrodynamic problem to a locally equivalent Hamiltonian system with a finite number of degrees.By studying the spectrum of the linearization at the equilibrium of the Hamiltonian,and its bifurcation diagram in the parameter plane,we obtain the homoclinic solutions of the reduced system which gives the solitary interfacial water waves.