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Dynamics of closed-form invariant solutions and formal Lagrangian approach to a nonlinear model generated by the Jaulent–Miodek hierarchy

  • Muhammad Usman , Akhtar Hussain ORCID logo EMAIL logo and Ahmed M. Zidan
Published/Copyright: February 11, 2025
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 80 Issue 3

Abstract

This study focuses on a (3 + 1)-dimensional nonlinear evolution model derived from the Jaulent–Miodek hierarchy. Our research employed analytical tools to scrutinize the invariance characteristics of this model. However, our primary emphasis is on utilizing the potent Lie group method, which effectively reveals the inherent symmetries within the model and explores solutions that remain invariant under group transformations using symmetry algebra. Furthermore, we investigated the application of Ibragimov’s approach to examine the conservation laws relevant to the model under consideration. This theorem is employed to identify and analyze the conservation laws associated with the (3 + 1)-dimensional nonlinear evolution model, which is essential for understanding the behavior of the system. Our research is significant as it contributes to exploring this particular model and addresses a specific gap in the group theoretic approach within this context.

Keywords: Lie group method; nonlinear evolution model; conservation laws; Lie algebra; Jaulent–Miodek hierarchy
Corresponding author: Akhtar Hussain, Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan, E-mail: 

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP.2/16/45.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The author states no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

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Received: 2024-11-03
Accepted: 2025-01-21
Published Online: 2025-02-11
Published in Print: 2025-03-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2024-0257
Keywords for this article
Lie group method; nonlinear evolution model; conservation laws; Lie algebra; Jaulent–Miodek hierarchy

Articles in the same Issue

  1. Frontmatter
  2. Chemical Physics
  3. Mathematical modeling for the potential energy of the aminophenol derivative azomethine molecule via Bezier surfaces and fuzzy inference system
  4. Topological descriptors and connectivity analysis of coronene fractal structures: insights from atom-bond sum-connectivity and Sombor indices
  5. Fundamental Concepts of Physical Science
  6. Stability analysis of semi-analytical technique for time-fractional Cauchy reaction-diffusion equations
  7. Dynamics of closed-form invariant solutions and formal Lagrangian approach to a nonlinear model generated by the Jaulent–Miodek hierarchy
  8. Solid State Physics & Materials Science
  9. Temperature-dependent elastic, mechanical, thermal, and acoustic behavior in alkaline earth semiconductors
  10. Investigation of the effect of Si content on the structural, mechanical, and tribological properties of TiAlN/AlSi protective multilayers
  11. Thermodynamics & Statistical Physics
  12. Higher-order corrections on the denaturation of homogeneous DNA thermodynamics
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