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Integrability Properties of the Slepyan–Palmov Model Arising in the Slepyan–Palmov Medium

Author

Listed:
  • Muhammad Usman

    (College of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), H-12, Islamabad 44000, Pakistan)

  • Akhtar Hussain

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • F. D. Zaman

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Asier Ibeas

    (Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain)

  • Yahya Almalki

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

Abstract

This study investigates the Slepyan–Palmov (SP) model, which describes plane longitudinal waves propagating within a medium comprising a carrier medium and nonlinear oscillators. The primary objective is to analyze the integrability properties of this model. The research entails two key aspects. Firstly, the study explores the group invariant solution by utilizing reductions in symmetry subalgebras based on the optimal system. Secondly, the conservation laws are studied using the homotopy operator, which offers advantages over the conventional multiplier approach, especially when arbitrary functions are absent from both the equation and characteristics. This method proves advantageous in handling complex multipliers and yields significant outcomes.

Suggested Citation

  • Muhammad Usman & Akhtar Hussain & F. D. Zaman & Asier Ibeas & Yahya Almalki, 2023. "Integrability Properties of the Slepyan–Palmov Model Arising in the Slepyan–Palmov Medium," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4545-:d:1273912
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