Asymptotics and stability of bifurcating solutions to the problem about the floating interface of two fluids

The asymptotics of bifurcating solutions in the case higher degenerations of linearized operator in the problem on capillary-gravity waves at the interface between two fluids is obtained. Group analysis methods in bifurcation theory under the group invariance conditions are applied. Criteria to the reduced stability of the bifurcating solutions are found.