On the nonlinear excitation in self gravitating quantum dusty plasma (Q2390827)

A self gravitating quantum dusty plasma is considered. The equations are given in a classical form with quantum corrections. The system of equations is composed of the equations of motion (of dust, ions and electrons), the corresponding equations of continuity, the Poisson equation for the gravitational potential (of dust, ions and electrons) and that for the electric potential (of ions and electrons). This system for densities, velocities and potentials (in one spatial dimension) is solved in a power series form of a parameter, equating the coefficients of the equal powers of the parameter in the equations gives the approximative equations. From the lowest order equations one gets two derived equations which are looking like Korteweg-de Vries (KdV) equations (containing some quantum mechanical corrections as well). These are reduced to linear KdV equations for which a linearized eigenvalue procedure is shown, together with a perturbation method around the soliton solution. The detailed analysis of the results are promised in a future publication.