Propagation of dust ion acoustic wave in a uniform weak magnetic field

Abstract

The effects of the obliqueness and the strength of the external magnetic field on the propagation ion acoustic wave in a dusty plasma are investigated. The dispersion relation of the electrostatic wave is found to be modified by the Lorentz force. The reductive perturbation technique is used to derive the equation of propagation of the electrostatic potential of the wave, known as the rotation-modified Korteweg-de Vries (rmKdV) equation. The time evolution of the electrostatic solitary wave, propagating obliquely to the background magnetic field, is numerically studied for different values of the right-hand side of the (rmKdV) equation. It is found that for small values of the right-hand side of the (rmKdV) equation, both compressive and rarefactive solitons undergo a decay by radiating energy to the tails, who themselves steepens to produce a secondary solitary wave who will in turn suffer another decay. This Scenario of decay and steepening is repeated indefinitely. However, for the high value of the right-hand side of the (rmKdV) equation, the soliton is unstable as it propagates and non-stationary waves must be formed.