DNLS solitons in collisional dusty plasma

Alfven waves are possible sources of turbulence in the interstellar medium. These waves are responsible for the transport of angular momentum and energy in the accretion discs. Such waves have been studied for last several decades in space plasmas. Most of the space plasmas are dusty. They contain charged grains and coupling of the grains to the magnetic field determines the wave propagation in the planetary and interstellar medium. In the present work, the nonlinear wave propagation in collisonal dusty plasma is considered. When the electrons and ions are highly magnetized and charged dust remains weakly magnetized, the relative drift between the dust and the plasma particles may significantly modify the wave characteristics in such a medium. It is shown that the collisonal dusty medium is inherently dispersive in nature and the balance between the dispersion and nonlinearity leads to derivative nonlinear Schrödinger (DNLS) equation. The relative drift between the charged grains and the plasma particles (electrons and ions) gives rise to the Hall diffusion in the medium. This Hall diffusion causes the wave dispersion. In many dusty plasma situations, Hall MHD is the only proper description of the plasma dynamics.