Studies of Rayleigh-Taylor instability of a thin liquid layer

On the basis of Lagrangian representation for equation of thin-liquid-layer dynamics, analytic solutions of the Rayleigh-Taylor instability problem at the nonlinear stage in the observer's space are found. Evolution of various perturbation types, in the layer shape and in layer velocity components, is considered. It is shown that there are both exponentially growing and limited oscillating solutions. The results of the theoretic considerations are substantiated with numerical calculations that use the complete system of the law of conservation.