Effects of Quantum Diffraction on the Propagation of E-A-W Solitary Structure in Fermi Plasma

TL;DR

This paper investigates how quantum diffraction influences the behavior of solitary wave structures in relativistic Fermi plasma, deriving a nonlinear Schrödinger equation and analyzing rogue wave stability through simulations.

Contribution

It introduces a quantum hydrodynamic model to derive a dispersion relation and nonlinear Schrödinger equation for relativistic quantum plasma, including quantum diffraction effects.

Findings

Quantum diffraction significantly affects solitary wave profiles.

Stable rogue wave solutions are identified and analyzed.

Simulations confirm the impact of plasma parameters on wave stability.

Abstract

Plasma state of matter can be studied in various types of situations. These studies are of great interest in Astrophysical objects like galaxies, accretion disk, neutron stars, etc, and laboratory plasma as well. Different objects demand different approaches to investigate the dynamics of the plasma. The relativistic effects in the motion of electrons in Quantum Plasma highly affect the characteristics of the solitary structure of the wave with two-temperature electrons. In this paper, considering the quantum hydrodynamic (QHD) model a dispersion relation is derived, and using standard perturbation technique, a mathematical model (i.e. nonlinear Schr\"odinger Equation) is studied for a wave with relativistic and quantum effects in it. We study the analysis for different values of diffraction coefficient, streaming velocity, and other plasma parameters as well. We analyze the stable rogue wave structure using NLSE and run simulations of those solitary profiles and rogue waves.