Solitons, envelope solitons in collisionless plasmas

A review is given to extensive development of theoretical, computational and experimental studies of nonlinear wave propagation in collisionless plasmas. Firstly, the historical experiment of Ikezi et al. is discussed in comparison with theoretical analysis based on the Korteweg-de Vries equation. Systematic discrepancy between the observation and the theoretical prediction suggests that it is necessary to examine such as higher order mode coupling effect and contribution of trapped particles. Secondly, effects of the nonlinear Landau damping on the envelope soliton of ion plasma wave is discussed on the basis of theoretical study of Ichikawa-Taniuti, experimental observation of Watanabe and numerical analysis of Yajima et al. Finally, a new type of evolution equation derived for the Alfven wave is examined in some detail. The rigorous solution obtained for this mode represents a new kind of envelope soliton, in which both of its phase and amplitude are subject to modulation of comparable spatial extension. In conclusion, the emphasis will be placed on the fact that much more intensive experimental researches are expected to be done, since the powerful methods to disentangle various nonlinear evolution equations are now available for theoretical approach