Multiple-scale Expansion for Nonlinear Ion-acoustic Waves
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By employing the multiple-scale expansion method, the present work examines non-linear waves in a cold collision less plasma, in the long-wave limit, and obtains a set of KdV equations governing various order terms in the perturbation expansion. By seeking a travelling wave type of solution to the evolution equations, a set of wave speeds associated with each time parameter are obtained. It is shown that the speed corresponding to the lowest order time parameter gives the wave speed of the conventional reductive perturbation method. The speeds corresponding to the higher order time parameters give the correction terms to the wave speeds of the classical reductive perturbation method.