Planar and nonplanar electron acoustic solitons in dissipative quantum plasma

The nonlinear propagation of electron acoustic waves (EAWs) in an unmagnetized dissipative quantum plasma is studied both in an unbounded planar geometry and a bounded nonplanar geometry. With the help of the reductive perturbation technique, damped Korteweg-de Vries (KdV), cylindrical and spherical KdV equations are derived by using the quantum hydrodynamic set of equations for EAWs. The linear dispersion relation is found to be modified by the collision between electrons and ions. The nondimensional parameter δ, the equilibrium density ratio of the cold to hot electron component, plays a crucial role in the formation of both compressive and rarefactive solitons. Approximate analytical time evolution solutions of planar and nonplanar damped KdV equations are presented. Numerically, the effects of several physical parameters on the properties of EAWs are discussed in the planar and nonplanar geometry. It is also found that electron acoustic solitons in the nonplanar geometry significantly differ from the planar geometry.