In the present work we consider the problem of free surface motion of the fluid with high dielectric constant in the strong horizontal electric field. It is shown that nonlinear surface waves can propagate nondispersively in the direction of electric field. Moreover, the counter-propagating solitary weakly nonlinear waves preserve the initial form after collision. The question arises as to whether the same tendency is observed for strongly nonlinear waves. We have shown that collisions of strongly nonlinear waves are elastic, i.e., the energy of solitary wave does not change. However, results of our numerical simulations indicate that, in general case, the interaction of strongly nonlinear waves leads to the shape distortion and formation of regions with high surface steepness.

This study was supported by the Russian Foundation for Basic Research (Project No. 14-08-31194), and by the Dynasty Foundation.