Nonlinear surface waves on a plasma layer

A nonlinear Schrödinger equation is derived which governs the nonlinear interaction of the adiabatic particle motion with finite-amplitude high-frequency surface waves traveling on an unmagnetized homogeneous plasma layer. The evolution equation has been obtained from the nonlinear dispersion relation of the waves (symmetric and antisymmetric modes, respectively) under the assumption that the high-frequency wave propagation is modified by slow motion. It is found that in limited ranges of the wave frequencies and wave numbers and for appropriate values of the parameter σ=${\omega }_p$a/c (${\omega }_p$ being the electron plasma frequency, a the layer half thickness, and c the speed of light), the finite-amplitude antisymmetric modes can propagate as supersonic or subsonic bright-envelope solitons. Under the same conditions, the symmetric surface waves prove to be modulationally stable and the nonlinear waves which can exist are dark-envelope solitons (envelope holes).