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Nonlinear stationary electron plasma waves are investigated in one-dimensional case. Full account is taken of the effects of both kinds of electrons which are trapped and untrapped in potential troughs. A condition for the existence of plasma waves which is periodic in space is obtained in the case that the amplitudes are sufficiently small. The waves are classified into harmonic and unharmonic waves. It is shown that while the electron distribution function for the former is continuous, that for the latter has a discontinuity. A dispersion relation for the harmonic waves which was obtained by Van Kampen is rederived.
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Kito et al. (1964) studied this question.
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