Numerical solution of KdV equation in dusty plasma system using Fourier transform

Abstract

We consider dusty plasma in a cometary environment comprising of positively and negatively charged dust ions, kappa distributed - solar electrons, cometary electrons and hydrogen ions. The existence of non linear waves such as solitons in these systems were explored in detail by various researchers analytically. In this article we solve the system numerically by deriving KdV equation and solving it using Fourier transform. Hence we study the generation and existence of solitons. We also explore the characteristics of the solitons formed by simulation of the system for various initial conditions. The system is found to have single soliton wave as exact solution and set of soliton wave train solutions for varied initial conditions. The soliton wave trains can be compressive, rarefactive or mixed in nature according to the initial condition. The simulation is helpful in understanding and modelling various dusty plasma systems.

Keywords

• KdV equation
• Solitons
• Dusty plasma
• Numerical solution
• Fourier transform