A wide class of nonlinear partial differential equations describing wave propagation in dispersive media is studied by using a method of multiple scales. It is investigated at first how the amplitude of a plane wave modulates itself in far-field. the result of the analysis shows that the system of equations may be classified into three types. For the case of the type 1 and the type 2A systems, the original system of equations can be reduced to a tractable single equation-a nonlinear Schrödinger equation. On the other hand, for the type 2B system, any simple reduced system cannot be obtained. Next investigated is the nonlinear modulation resulting from interactions between a plane wave and a slowly varying wave for the type 2A and the type 2B systems. It is found that such a nonlinear modulation shows a very different nature from each other for these two systems.
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Inoue et al. (1974) studied this question.
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