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Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of ion acoustic wave. The basic set of fluid equation is reduced to a coupled set of the Korteweg-de Vries equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been examined in details.
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Ichikawa et al. (1976) studied this question.
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