Dynamics of space debris induced, accelerated, nonlinear ion acoustic waves in presence of kinematic viscosity

This work shows a detailed analytical and numerical investigation of the propagation of (1+1) dimensional, long wavelength, nonlinear, ion-acoustic waves in a collisionless, unmagnetized, homogeneous plasma considering kinematic viscosity and charged debris particles in space. The debris charge density is considered to be very small compared to the density of plasma. The forced KdV-Burger equation governs the dynamics of nonlinear ion-acoustic waves with viscous effects where the forcing term arises due to the debris particles. The exact, shock wave solutions pinned with their corresponding debris functions having constant and time-varying velocities have also been evaluated. All these exact solutions moving with the debris function with the same velocity are called “pinned shock waves.” The stability of the exact accelerated shock wave solutions has been analyzed using linear stability analysis. We have derived analytically the generation of precursor solitons for a weak Gaussian debris function and examined the effect of kinematic viscosity on those precursor solitons. We have also derived few approximate solitary wave solutions in presence of the self consistent, weak debris function and viscous effects. We have numerically solved the forced KdV Burger equation for a Gaussian debris profile and shown the effects of kinematic viscosity on the generation of precursor solitons. As far as our study goes, such analytical and numerical investigation in this context has not been done before in literature.