Higher order contribution to ion-acoustic Korteweg–de Vries (KdV) soliton in unmagnetized quantum plasmas with arbitrary degeneracy of electrons

Abstract

The propagation of nonlinear ion-acoustic Korteweg–de Vries (KdV) solitons and dressed solitons (with higher order contribution term) in unmagnetized quantum plasmas with arbitrary degeneracy of electrons is investigated using quantum hydrodynamic model. The reductive perturbation method is used to derive the first order nonlinear ion-acoustic KdV equation and also higher order contribution of inhomogeneous differential equation is obtained for the dressed ion-acoustic wave soliton in arbitrary degenerate electron plasmas. Moreover, the higher order inhomogeneous differential equation is solved (nonsecular solution is obtained) using the renormalization method. The conditions for the validity of the higher order correction are also discussed in detail for ion-acoustic solitons in unmagnetized arbitrary degenerate electrons plasma case. The effects of chosen values of electron temperature, equilibrium fugacity and corresponding electron density of a physical quantum plasma system and quantum diffraction parameter H (for two conditions i.e., H < 2 or H > 2) on the amplitude and width of the KdV and dressed ion-acoustic wave solitons for both electrostatic potential hump (compressive) or dip (rarefactive) structures are investigated. The numerical plots are also presented for illustration with numerical values of a physical partially degenerate electrons plasma system exist in the astrophysical or laboratory conditions.