Finite-amplitude waves on the surface of a viscous deep liquid

For the first time a rigorous solution to the problem on time evolution of the periodic wave shape on the surface of a viscous infinitely deep liquid is found in the quadratic approximation with respect to the wave amplitude. It is found, in particular, that the damping rate of the quadratic component with respect to the wave amplitude is twice as high as the damping rate of the linear term. It is shown that inclusion of viscosity leads to asymmetry of the wave profile.