Topics on Solitons in Plasmas

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Abstract
Solitons can be regarded as "nonlinear normal modes", in terms of which dynamical properties of a given physical system could be analyzed. The author, however, points out firstly that the cnoidal wave is also the genuine nonlinear wave playing important roles in nonlinear phenomena in plasmas and other dispersive media. Explicit analysis for the ion acoustic cnoidal wave is carried out up to the second order on the basis of Kodama-Taniuti's renormalized reductive perturbation theory. The nonlinear ion flux associated with the cnoidal wave is shown to have different dependence on the wave amplitude as compared with the quasi-linear ion flux. At the same time, it should be noticed that the nonlinear ion flux also exhibits profound frequency dependence, which is not predicted by the quasi-linear treatment. Secondly Bogoliubov-Mitropolsky perturbation analysis of the perturbed envelope soliton is briefly discussed referring to Karpman-Maslov's perturbation approach based on the inverse scattering method. Thirdly, brief summaries on plasma waves in magnetized plasmas are followed by a report on the new inverse scattering scheme for the derivative nonlinear Schrödinger equation. In concluding remark, the potential importance of researches on solitons in strong plasma turbulence has been emphasized.