The instability of plane envelope Langmuir solitons subject to transverse perturbations is reconsidered for the cubic nonlinear Schr\"odinger equation as well as the coupled set of high- and low-frequency equations in the case of nonadiabatic ion response. The nonlinear investigation demonstrates instability with a cutoff in all cases and predicts a drastic lowering of the instability growth rates when nonadiabatic ion motion is allowed for. Our analytical results agree with recent numerical computations.
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Laedke et al. (1978) studied this question.