By using slow space-time variation of the amplitude, a pair of coupled nonlinear Schrodinger equations are derived from the equation of continuity, fluid equation of motion with collisional damping effects for both electron and ion, and the Poisson equation. If the collisional damping effect is neglected then localized solitary wave solutions exist for certain wave numbers of high frequency oscillation with a range of low-frequency wave numbers. Among these localized solitary wave solutions some are found to be stable. The basic balance equations for the solution parameters have been derived from the evolution equations. It is found that the width and wave numbers of the solitary wave remain constant while in motion.
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