Adiabatic theory for a single nonlinear wave in a Vlasov plasma

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Abstract
A large-amplitude high-frequency modulated wave launched by an external source significantly changes the plasma equilibrium. The adiabatic Vlasov distribution function of the electrons is found for one-dimensional initial-and boundary-value problems. The nonlinear dispersion relation is derived to all orders in the electric-field amplitude. A new nonlinear mode below the electron plasma frequency exists. In this state the plasma is described by a double-humped distribution function.