A nonlinear Schr\"odinger equation is derived which governs the nonlinear interaction of the adiabatic particle motion with finite-amplitude ion-acoustic waves in an unmagnetized plasma. It is found that the ion-acoustic waves remain modulationally stable and that the nonlinear wave can propagate in the form of dark envelope solitons.
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P. K. Shukla (1986) studied this question.
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