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Application scope of the reductive perturbation method to derive the KdV equation and CKdV equation in dusty plasma

Published online by Cambridge University Press:  17 April 2023

Heng Zhang*
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Yu-Xi Chen
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Lin Wei
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Fang-Ping Wang
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Wei-Ping Zhang
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Wen-Shan Duan*
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Email addresses for correspondence:,
Email addresses for correspondence:,


The application scopes of two different reductive perturbation methods to derive the Korteweg–de Vries (KdV) equation and coupled KdV (CKdV) equation in two-temperature-ion dusty plasma are given by using the particle-in-cell (PIC) numerical method in the present paper. It suggests that the reductive perturbation method (RPM) is valid if the amplitude of the CKdV solitary wave is small enough. However, for the KdV solitary wave, RPM is valid not only if the amplitude of the KdV solitary wave is small enough, but also if the nonlinear coefficient of the KdV equation is not tending to zero.

Research Article
Copyright © The Author(s), 2023. Published by Cambridge University Press

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