Time evolution of an unstable soliton solution to dust acoustic plasma with trapped electrons

Abstract

The positive dust charged grains is considered as the immobile particles compared to ions and electrons. Using the assumption that some electrons can be trapped in the dust charge potential while others move freely in the plasma with external magnetic field. The reductive perturbation method shows that the weakly nonlinear waves equation gives a soliton solution. The spectral method is applied for the time evolution of the perturbed soliton solution to the sinusoidal function with the long-wavelength. This shows that the unstable plane soliton will be transformed into the higher dimensions.