Exploration of soliton solutions and dynamical analysis of the q-form Zhanbota equation: An application to image encryption

Peiluan Li, Rui Qiao, Changjin Xu, Miaoran Yiao, Yizhen Qu and Shabir Ahmad

Physica A: Statistical Mechanics and its Applications, 2025, vol. 675, issue C

Abstract: In this paper, the Zhanbota-IIA equation is investigated via dynamical analysis and soliton theory. The Zhanbota-IIA equation is transformed into a coupled system of ordinary differential equations by using a Galilean transformation. Bifurcation analysis is carried out to show behavior of equilibrium points. The proposed system exhibits multi-stability, characterized by a mixture of periodic and chaotic behaviors. The power spectrum analysis and return maps along with recurring plots of the governed system are displayed. Time series, Poincaré section and strange attractors with suitable delay parameter are visualized to illustrate more dynamical behavior. We provide an application in image encryption utilizing the proposed nonlinear system to scramble and diffuse the image pixels, thereby enhancing security. The modified Exp-function technique is utilized to derive different soliton solutions of the considered Zhanbhota equation. We obtain periodic, breather, bright and dark solitons, which are displayed in 3D graphs.

Keywords: Zhanbhota-IIA equation; Bifurcation; Chaos; Multi-stability; Solitons (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437125004613
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

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:eee:phsmap:v:675:y:2025:i:c:s0378437125004613

DOI: 10.1016/j.physa.2025.130809

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().