Abstract
Theory of amplitude modulation of plasma wave is developed by applying the Karpman-Krushkal theory of quasi-monochromatic wave propagation in nonlinear-dispersive media to the Vlasov plasma. As a result of careful analysis of nonlinear resonant effect between wave and particles, it is shown that the modulation of complex amplitude A (x, t) of the potential wave in plasmas is described by the modified nonlinear Schrodinger equation i (∂/∂t+λ∂/∂x) A+p∂2/∂x2A+q|A|2A+s_??_/π∫|A (x', t)|2/x-x'dx'A+irA=0
Where λ is the group velocity of the wave. The coefficients q and s involves contributios of the resonant interaction of particles and wave at the group velocity, while the coefficient r represents the linear Landau damping rate, and P ex presses the dispersion effect defined as (1/2) ∂λ/∂k.
