Comprehensive analysis of a magneto-electro-elastic longitudinal wave model: symmetries, chaos, and soliton structures
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Sonia Akram
Abstract
This study offers a comprehensive analysis of a modified (1 + 1)-dimensional longitudinal wave equation (LWE) tailored to explain the nonlinear dynamic structure of a magneto-electro-elastic (MEE) circular rod. The model presents the coupled interactions of electrical and magnetic fields and mechanical interactions by including physical characteristics such as stress-strain and mass density relationships, reflecting deeper insight into the propagation of longitudinal waves in MEE material. To exhibit the symmetry structure of the equation, Lie symmetry analysis approach is used, producing symmetry reductions that reduce the original partial differential equation into ordinary differential systems. Beyond the symmetry system, the dynamics of the model is methodically analyzed through different diagnostic tools, such as multistability analysis, bifurcation diagrams, power spectrum plots, heterogeneous recurrence plots, Lyapunov exponent evolution, and strange attractor representations, capturing rich chaotic dynamics and sensitive dependence on distinct initial conditions. Additionally, we create novel exact solutions of the proposing equation using two advanced symbolic techniques namely, the generalized Ansatz method and the Painlevé–Paul method to derive a wide spectrum of wave profiles, including kink, anti-kink, periodic, W-shaped, and mixed-type solutions. The importance of this work lies in its unified analysis of symmetry, chaos, and soliton theory within a physically motivated structure, inproving our understanding of nonlinear wave propagation in magneto-electro-elastic structures and providing valuable tools for modeling complex materials in applied physics and engineering contexts.
Funding source: Princess Nourah bint Abdulrahman University, Riyadh, Saudi ArabiaArabia
Award Identifier / Grant number: PNURSP2025R443
Acknowledgments
Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R443), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R443), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
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Data availability: Not applicable.
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