Investigation of Nonlinear Dynamics and Stability Analysis of Dust Acoustic Shock Waves in a Quantum Dusty Plasma

Emadi, Elham; Pourjafari, Neda

doi:10.30473/jphys.2024.72259.1213

Document Type : Research

Authors

Elham Emadi ¹
Neda Pourjafari ²

¹ Sahand university of technology

² Department of Chemical, Petroleum and Gas Engineering, Technical and Vocational University, Tehran,Iran

https://doi.org/10.30473/jphys.2024.72259.1213

Abstract

In this article, using quantum hydrodynamic (QHD) model, dust acoustic (DA) shock waves are studied in a quantum dusty plasma containing degenerate electrons, ions and negatively charged dust grains. By employing the reductive perturbation technique, a Kortweg-de Vries-Burgers (KdVB) equation is derived and solved theoretically and numerically. The hyperbolic tangent (tanh) method is used for theoretical solution. This method is one of the most convenient approaches for solving the nonlinear partial differential equation in dispersive and dissipative systems. The KdVB equation is solved numerically using the fourth-order Runge – Kutta method. It found that when dissipation dominates over dispersion, monotonic shock structure is formed, while in the case of small dissipation, oscillatory shock profile created. The influence of viscosity on DA shock waves shows that shock thickness enhanced with the increase in viscosity. Additionally, the number and height of oscillatory shocks increase as viscosity decreases. The solutions of the KdVB equation studied in a frame moving with the phase velocity of the wave. Considering the boundary conditions, the nonlinear obtained equation rewrite in the form of a dynamical system. In the plane, this system has two fixed points. Investigating the eigen values corresponding to these ﬁxed points indicate that one point is always a saddle, while the other is either a stable focus or a stable node. The phase plane analysis shows that the decrease in the number of spirals shows increase in dissipation.

Keywords

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Quarterly Journal of Optoelectronic

Investigation of Nonlinear Dynamics and Stability Analysis of Dust Acoustic Shock Waves in a Quantum Dusty Plasma

References

References

Volume 7, Issue 3 - Serial Number 20
April 2025
Pages 31-40

Investigation of Nonlinear Dynamics and Stability Analysis of Dust Acoustic Shock Waves in a Quantum Dusty Plasma

References

References

Volume 7, Issue 3 - Serial Number 20April 2025Pages 31-40

Volume 7, Issue 3 - Serial Number 20
April 2025
Pages 31-40