Propagation and Head-On Collision of Dust Acoustic Waves in Collisional Dusty Plasma: the Saturn Main Rings

The propagation characteristics and the consequences of head-on collision of dust acoustic waves (DAWs) are studied considering unmagnetized collisional dusty plasma comprising negatively mobile charged dust grains, Maxwellian electrons, inertial positively charged ions, and immobile neutral particles. The consequences of head-on collision along with the productions of phase shifts of two-sided Kortewg-de Vries (KdV) equations are studied using extended Poincaré-Lighthill-Kue (ePLK) method. While the propagation properties of DAWs are studied using modified KdV (mKdV) equation employing reductive perturbation method. The typical physical parameters are considered pertinent to the Saturn A, B, and C rings. The compressive and rarefactive dust acoustic (DA) solitons (DASs) are produced depending on the plasma parameters concerned in the Saturn rings. The negative phase shift increases with the increase of ion density, while the negative phase shifts decreases with increasing the density of charged dust grains. The modified KdV (mKdV) soliton propagates toward right direction. The DASs satisfy the principle of superposition in the colliding region.