Nonlinear Wave Structures, Multistability, and Chaotic Behavior of Quantum Dust-Acoustic Shocks in Dusty Plasma with Size Distribution Effects

Huanbin Xue and Lei Zhang ()
Additional contact information
Huanbin Xue: School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China
Lei Zhang: School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China

Mathematics, 2025, vol. 13, issue 19, 1-22

Abstract: This paper presents a detailed study of the ( 3 + 1 ) -dimensional Zakharov–Kuznetsov–Burgers equation to investigate shock-wave phenomena in dusty plasmas with quantum effects. The model provides significant physical insight into nonlinear dispersive and dissipative structures arising in charged-dust–ion environments, corresponding to both laboratory and astrophysical plasmas. We then perform a qualitative, numerically assisted dynamical analysis using bifurcation diagrams, multistability checks, return maps, Poincaré sections, and phase portraits. For both the unperturbed and a perturbed system, we identify chaotic, quasi-periodic, and periodic regimes from these numerical diagnostics; accordingly, our dynamical conclusions are qualitative. We also examine frequency-response and time-delay sensitivity, providing a qualitative classification of nonlinear behavior across a broad parameter range. After establishing the global dynamical picture, traveling-wave solutions are obtained using the Paul–Painlevé approach. These solutions represent shock and solitary structures in the plasma system, thereby bridging the analytical and dynamical perspectives. The significance of this study lies in combining a detailed dynamical framework with exact traveling-wave solutions, allowing a deeper understanding of nonlinear shock dynamics in quantum dusty plasmas. These results not only advance theoretical plasma modeling but also hold potential applications in plasma-based devices, wave propagation in optical fibers, and astrophysical plasma environments.

Keywords: Zakharov–Kuznetsov–Burgers equation; shock waves; bifurcation analysis; Lyapunov exponents; chaotic attractors; multistability; Poincaré maps; Paul–Painlevé approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/19/3101/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/19/3101/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:19:p:3101-:d:1759744

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().