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The relativistic equations governing the nonlinear interaction of two light waves and a Langmuir wave are shown to admit two classes of solitary-wave solutions. Temporal solitary waves propagate at speeds greater than the speed of light and carry no information. Spatial solitary waves propagate at speeds less than the speed of light and do carry information. The properties of these waves are discussed and the spatial solitary waves are shown to be well suited to the beat-wave acceleration of particles.
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McKinstrie et al. (1986) studied this question.
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