Existence of large amplitude periodic waves in two-fluid flows of infinitedepth

Two-dimensional periodic traveling gravity waves in a two-fluid ow are cons idered, where the ow has no rigid boundaries. Each fluid is inviscid, incom pressible, and irrotational and the density ratio of the upper fluid to the lower fluid is between zero and one. The governing equations are rst trans formed into a single nonlinear integral equation using the Hilbert transfor m and the corresponding integral operator is compact in certain Banach spac es after a cut-off function is introduced. By a global bifurcation theorem, it is shown that there exist periodic waves of large amplitude on the inte rface until either the bifurcation parameter goes to infinity or the functi on of th wave pro le and its first-order derivative are not in the classica l Holder space. It is also noted that the nonlinear integral equation is ve ry general and can be used to study the waves of large amplitude numericall y.