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

Author

Listed:
  • Li, Peiluan
  • Qiao, Rui
  • Xu, Changjin
  • Yiao, Miaoran
  • Qu, Yizhen
  • Ahmad, Shabir

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.

Suggested Citation

  • Li, Peiluan & Qiao, Rui & Xu, Changjin & Yiao, Miaoran & Qu, Yizhen & Ahmad, Shabir, 2025. "Exploration of soliton solutions and dynamical analysis of the q-form Zhanbota equation: An application to image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 675(C).
    • Handle: RePEc:eee:phsmap:v:675:y:2025:i:c:s0378437125004613
    DOI: 10.1016/j.physa.2025.130809
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    References listed on IDEAS

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    1. Iskakova, Kulpash & Alam, Mohammad Mahtab & Ahmad, Shabir & Saifullah, Sayed & Akgül, Ali & Yılmaz, Gülnur, 2023. "Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 219-245.
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    Cited by:

    1. Samina, Samina & Wali, Samad, 2026. "Chaotic dynamics and Lyapunov analysis of the Benney–Luke equation for image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 683(C).

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