Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a twocomponent electron–ion dense quantum plasma. Using standard perturbation technique, a nonlinear Schrödinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects significantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.

In this paper,we have meticulously studied the amplitude modulation of electron-acoustic waves and the formation and properties of envelope solitons in a five-component complex plasma containing statistically kappa distributed warm and cold electrons, kappa-distributed positrons and Boltzmann-distributed positive and negative ions. The picture considered here is very similar to solar atmosphere and planetary environments. The parametric dependence of modulational instability on kappa index, positron and electron densities, ion and reciprocal of positron temperatures has been studied in detail and the findings obtained here will be beneficial for further astrophysical investigations.

In this paper we have made use of reductive perturbation technique (RPT) and carried out homotopy analysis method (HAM) to investigate the effect of exchange correlation and quantum diffraction on the electrostatic waves in quantum magnetoplasma. We have derived a nonlinear Schrödinger equation (NLSE) by using RPT that describes the spatiotemporal evolution of an initial waveform. Apart from this technique, we have made use of HAM to second our initial findings. It has been shown that both quantum diffraction $H$ and parameter streaming velocity $u_0$ have significant effects in determining the stability criteria and the growth or decay of any instability created therein. The stable parametric regimes are crucial from the experimental point of view as well.