The reductive perturbation method developed in Part I of this series is applied to plasma waves with long wavelength, where the fluid model will be used throughout. As typical examples, we consider the ion-acoustic, magneto-acoustic, and Alfvén waves. The ion-acoustic wave belongs to the ordinary case to which the general theory can directly be applied, while the magneto-acoustic and Alfvén waves belong to the exceptional cases noted in Part I.
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Tsunehiko Kakutani (1974) studied this question.