A nonlinear boundary value problem on the propagation of surface waves in a layer of viscous incompressible fluid of infinite depth is considered. Equations of motion and boundary conditions are written. The solution of the problem is found by the small parameter method. An expression for the damping decrement of the wave oscillations is obtained. The program code in C++ for the numerical study of the propagation of nonlinear waves on the surface of a viscous liquid is developed.

Keywords: viscous liquid, slabowska fluid, nonlinear surface waves, the damping rate of waves, phase velocity, frequency wave

The dependence of the values characterizing the propagation of nonlinear waves on the surface of a liquid conductor on the electric field strength and on the wavelength is described. Electrohydrodynamic waves are investigated, namely, the motion of drops, convective motion of liquid, deformation of drops and bubbles in the applied electric field, propagation of surface waves in a linear approximation are considered. A mathematical model of nonlinear wave propagation on the charged surface of a liquid conductor is constructed. The graphs of the dependence of the wave oscillation frequency on the electric field strength and phase velocity on the wavelength are plotted.

Keywords: nonlinear surface waves, liquid conductor, dielectric constant, phase velocity, magnetic field strength, surface charge