A method for higher-order expansion in non-linear ion-acoustic waves
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The basic equations describing the non-linear ion-acoustic waves in a cold collisionless plasma, in the longwave limit, is re-examined through the use of a modified multiple-scale expansion method. Expanding the field quantities into a power series of the smallness parameter epsilon, a Set Of evolution equations is obtained for various terms in the perturbation expansion. To illustrate the present derivation, a localized travelling wave solution is studied for the derived field equations and the result is compared with those of Malfliet and Wieers (J. Plasma Phys. 56 (1996) 441-450), who employed the dressed solitary wave approach from the outset of their study.