An application of multiple-time scale perturbation method to nonlinear ion-acoustic waves
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In this work, by utilizing the multiple-time scale expansion method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. By defining a single time parameter we showed the connection of the modified reductive perturbation method to the multiple-time scale expansion method.