Nonlinear surface waves on a tangential discontinuity in magnetohydrodynamics

On Gravity Waves on the Surface of Tangential Discontinuity

On the basis of critical analysis of literature it is shown that the existing theory of surface gravity waves is incorrect and contradictory. Based on the new results published by the author dispersive equation for linear waves generated on the surface of tangential discontinuity between air and water was obtained. It is demonstrated that this equation is applicable only to capillary waves and ...

Nonlinear waves on the surface of a dielectric liquid in a strong tangential electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope angles. It is established that the equation can be solved for liquids with sufficiently high values of the permittivity. This makes it possible to describe the in...

On Nonlinear Water Waves in a Channel

on nonlinear water waves in a channel

Nonlinear Hyperbolic Surface Waves

We describe examples of hyperbolic surface waves and discuss their connection with initial boundary value and discontinuity problems for hyperbolic systems of PDEs that are weakly but not uniformly stable.