A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua. (Q1589885)

The author studies 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, the author describes the solution set of the equation for the selection of values of the parameters present and allows for possible imperfections in the resonance.