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

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. Fir...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 21; p. 4545
Main Authors Usman, Muhammad, Hussain, Akhtar, Zaman, F. D., Ibeas, Asier, Almalki, Yahya
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2023
Subjects
Behavior
Conservation laws
homotopy operator
Laws, regulations and rules
Lie groups
Lie symmetry method
longitudinal wave
Longitudinal waves
Mechanics
Multipliers
Operators (mathematics)
optimal system
Oscillators
Partial differential equations
Symmetry
the Slepyan–Palmov model
Wave propagation
Germany
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11214545