Nonlinear wave on the surface layer of a viscous liquid

The nonlinear problem of the propagation of waves on the free surface of the layer of viscous incompressible fluid of infinite depth in the plane case. Using small parameter method, this nonlinear problem is decomposed into problems in the first two approximations that consistently allowed. Nonlinear expressions for the components of the velocity vector, the dynamic pressure and the shape of the free surface. The motion of particles of the viscous fluid caused by the spread of the wave of the free surface. It is found that the viscosity has a significant effect on the shape of the trajectories of liquid particles which is manifested as a decrease in the amplitude of oscillation over time, and in contrast to the paths near the free surface and penetration. The nonlinear effect of Stokes, which is the presence of near-surface currents.