Solitary waves in self-gravitating dusty plasma

The electrostatic dust acoustic wave is studied in a uniform gravitating dusty plasma, when the self-gravitation does alter the linear modes given by the dispersion relation. It is observed that instead of a single nonlinear equation we get two coupled KdV-like systems. It is observed that such a system can sustain solitary-wave-like excitations under suitable conditions on the plasma parameters. Such an analysis is very important in ascertaining the fate of a grain orbiting around a magnetized planet in space, where there is a competition between magnetic and gravitational forces. And this in turn gives rise to the question of magnetogravitational instability, which plays an important role in star formation. It is observed that the gravitational soliton's amplitude, being proportional to the Jeans frequency, is always smaller compared to the electrostatic counterpart.