A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua

摘要

In this paper we study the capillary-gravity profiles which may occur at the interface of two fluids when the fundamental mode and its third harmonic interact with each other. The problem is treated as one in bifurcation theory by transforming it into a nonlinear operator equation between suitable function spaces. Using classical analytic methods and by exploiting the group invariances of the operator, we are able to describe the solution set of the equation for a selection of values of the parameters present and to allow for possible imperfections in the resonance.