Phase Shift of KdV Soliton Associated with Collision Phenomena of Force KdV Solitons and Analysis of Time Fractional Ion-Acoustic Dusty Plasma Waves in the Earth’s Magnetosheath

Abstract

Magnetized three-component dusty plasma consisting of inertial ions and two electron populations at different temperatures obeying a kappa distribution is used to investigate the phase shifts of the Korteweg-de Vries (KdV) solitons, collision phenomena, and formation of force KdV (FKdV) solitons in the presence of an external periodic force and the time fractional (TF) KdV (TFKdV) solitons of first- and second-order approximate, as well as the formation of electric field structures in the Earth’s magnetosheath region. The KdV phase shifts due to the head-on collision of ion-acoustic waves (IAWs) are derived using the extended Poincaré-Lighthill-Kuo (ePLK) technique. The KdV equation is subsequently converted into a TFKdV equation by following the process of El-Wakil et al. (El-Wakil S A, Abulwafa E M, Zahran M A, Mahmoud A A. Nonlinear Dyn 2011; 65: 55) for right-traveling IAWs. By adding a source term with strength to the KdV equation, the FKdV equation is determined for right-traveling IAWs. Due to the effects of the relevant parameters in the mentioned environment, compressive (hump-shaped) and rarefactive (dip-shaped) FKdV solitons are formed, together with positive and negative phase shifts. Here, only a positive phase shift is studied. The FKdV ion-acoustic solitons follow the superposition principle in the collision processes. The rarefactive and compressive (dip-shaped and hump-shaped) electric field structures are produced due to the effects of traveling wave velocity and the TF parameter.