System of Laplace equations in a half-space with a free interface, capillary-gravitational waves, bifurcation, and symmetry

摘要

We study the stability of branching solutions of a system of two nonlinearly perturbed Laplace equations in a half-space with two differential relations on the interface. This system describes the motion of a two-layer fluid. To construct and study the related branching systems, methods of group analysis of differential equations (RZhMat 1978 11B883K, RZhMat 1983 11A813K) and the S. Lie-L.V. Ovsyannikov technique of invariants and invariant manifolds are used.