A Modified Reductive Perturbation Method as Applied to Nonlinear Ion-Acoustic Waves

Abstract

The basic equations describing the nonlinear ion-acoustic waves in a cold collisionless plasma, in the longwave limit, is re-examined through the use of a modified reductive perturbation method. Introducing the concept of a scale parameter and expanding the variables and the scale parameter into a power series of the smallness parameter ε, a set of evolution equations is obtained for various order 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 obtained by Sugimoto and Kakutani [rf:3] who introduced some slow scales, Kodama and Taniuti [rf:4] who employed the renormalization method and Malfliet and Wieers, [rf:6] who employed the dressed solitary wave approach from the outset of their study.