A theory of the amplitude modulation of quasi-monochromatic nonlinear plasma waves

A theory of the amplitude modulation of plasma waves is developed by applying the Karpman-Krushkal theory of quasi-monochromatic wave propagation analysis of the nonlinear wave-particle resonant effect leads to the modified nonlinear Schrüdinger equation with a non-local nonlinear term, which has been independently derived by Ichikawa & Taniuti on the basis of a reductive perturbation approach. The effect of the non-local nonlinear term is described explicity by investigating the modulation instability of an ion plasma wave.