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The collinear propagation of an arbitrary number of finite-amplitude waves is modeled by a system of coupled nonlinear Schr\"odinger equations. This model incorporates the effects of a coordinate-dependent external potential and coordinate-independent nonlinearities. A virial theorem is derived, which governs the nonlinear focusing of these coupled waves. For two light waves in a beat-wave accelerator, the coupling to each other and to the resonantly generated Langmuir wave has a significant effect on the focusing properties of the waves.
McKinstrie et al. (1988) studied this question.
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