Ion-acoustic cnoidal waves in a quantum plasma

TL;DR

This paper investigates nonlinear ion-acoustic cnoidal waves in unmagnetized quantum plasmas, deriving solutions using the Korteweg-de Vries equation and analyzing how quantum effects influence wave structures and properties.

Contribution

It introduces a novel analysis of ion-acoustic cnoidal waves in quantum plasmas using the reductive perturbation method and Sagdeev pseudo-potential, highlighting quantum parameter effects.

Findings

Both compressive and rarefactive wave structures are identified.

Wave wavelength and frequency depend on nonlinear wave amplitude.

Quantum parameter influences wave structure formation.

Abstract

Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave solutions are obtained. The corresponding analytical solution and numerical plots of the ion-acoustic cnoidal waves and solitons in the phase plane are presented using the Sagdeev pseudo-potential approach. The variations in the nonlinear potential of the ion-acoustic cnoidal waves are studied at different values of quantum parameter $H_{e}$ which is the ratio of electron plasmon energy to electron Fermi energy defined for degenerate electrons. It is found that both compressive and rarefactive ion-acoustic cnoidal wave structures are formed depending on the value of the quantum parameter. The dependence of the wavelength and frequency on nonlinear wave amplitude is also presented.