Fully nonlinear capillary–gravity wave patterns under the tangential electric field

Two-dimensional fully nonlinear capillary–gravity traveling waves are studied when a uniform electric field is applied in a direction parallel to the undisturbed free surface of a conducting fluid. For simplicity, we make assumption that the permittivity of the fluid is much larger than that of the up-layer gas. Therefore this two-layer problem can be reduced to a one-layer one, such that only in the fluid domain and its free boundary, the governing equations need to be solved. Fully localized solitary waves are found numerically via conformal mapping technology and direct continuation method. Unlike general capillary–gravity solitary waves on deep water that its depression branch can exit down to zero speed whilst these waves develop self-intersection points and become unphysical at low speed, under the external electric field wave-packet solitary waves can only exist at finite translating speed.