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

Muhammad Usman, Akhtar Hussain, F. D. Zaman, Asier Ibeas () and Yahya Almalki
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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

Mathematics, 2023, vol. 11, issue 21, 1-13

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.

Keywords: Lie symmetry method; the Slepyan–Palmov model; optimal system; longitudinal wave; conservation laws; homotopy operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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