Study of Real Dispersion Relation and Shock Profile of Electron Acoustic Wave in Fermi Plasma at Critical Regime

In this paper, the linear and non- linear properties of electron acoustic waves in a collision less Fermi plasma is investigated analytically by employing Quantum Hydrodynamic (QHD) model. The plasma system taken into account consists of hot and cold electrons and ions. By using standard reductive perturbation method the modified Korteweg-de Vries Burgers equation (MK-dVB) is derived in order to study the shock profile of electron acoustic waves numerically in a viscous plasma at the critical regime. Standard soliton solutions are used for quantitative and qualitative study of spatial and temporal evaluation of shock waves