Interaction of strongly nonlinear waves on the free surface of a dielectric liquid in a horizontal electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid with a large relative permittivity in a strong horizontal electric field has been considered. It has been demonstrated that the interaction between oppositely propagating solitary waves in arbitrary geometry is elastic: they conserve their energy and momentum. The interaction between waves has been numerically simulated with the use of conformal variables. It has been shown that the interaction deforms the waves; this effect is weak for waves with a relatively small amplitude: deformation for oppositely propagating waves with the identical shape is determined by the fourth power of their amplitude. At multiple collisions of strongly nonlinear waves, a tendency to the formation of singularities, i.e., points with a high energy density of the field, is observed.