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Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory

Author

Listed:
  • Hassan Almusawa

    (Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia)

  • Adil Jhangeer

    (IT4Innovations, VSB—Technical University of Ostrava, Poruba, 708 00 Ostrava, Czech Republic
    Department of Mathematics, Namal University, 30 km Talagang Road, Mianwali 42250, Pakistan)

Abstract

This study introduces the KdV–Caudrey–Dodd–Gibbon (KdV-CDGE) equation to describe long water waves, acoustic waves, plasma waves, and nonlinear optics. Employing a generalized new auxiliary equation scheme, we derive exact analytical wave solutions, revealing rational, exponential, trigonometric, and hyperbolic trigonometric structures. The model also produces periodic, dark, bright, singular, and other soliton wave profiles. We compute classical and translational symmetries to develop abelian algebra, and visualize our results using selected parameters.

Suggested Citation

  • Hassan Almusawa & Adil Jhangeer, 2024. "Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2242-:d:1438057
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    References listed on IDEAS

    as
    1. Jhangeer, Adil & Hussain, Amjad & Junaid-U-Rehman, M. & Baleanu, Dumitru & Riaz, Muhammad Bilal, 2021. "Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Yang Yang & Jian-ming Qi & Xue-hua Tang & Yong-yi Gu, 2019. "Further Results about Traveling Wave Exact Solutions of the (2+1)-Dimensional Modified KdV Equation," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-10, May.
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