New nonlinear eigenmodes of a self-gravitating spherical charged dust molecular cloud

We present a nonlinear stability analysis for an idealistic field-free hydrodynamic model of a self-gravitating massive charged dust molecular cloud in the presence of dust grain velocity convection. Identical spherical dust grains are equally charged, but the cloud as a whole is electrically neutral on the Jeans scale. Application of a multiscale analytical method shows that the self-gravitational potential fluctuation dynamics is governed by a new type of modified Korteweg?de Vries?Burger equation that has a self-consistent linear driving derivative source arising from dust flow convection. A detailed numerical analysis of the eigenmode structures in the steady state is carried out. It is found that the self-gravitational potential fluctuations contribute in the form of new oscillatory shock-like structures because of gravito-electrostatic coupling. The distinctive features of the eigenmode profiles are discussed in detail. In addition, the main conclusions relevant to the astrophysical context are briefly presented.