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Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state

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  • Karna, Ashutosh Kumar
  • Satapathy, Purnima

Abstract

In this article, the well-known Cargo–Leroux model with isentropic perturbation equation of state is analyzed using the Lie symmetry method. By using invariant conditions of system of partial differential equations, six dimensional Lie algebra is obtained. The optimal system for system of partial differential equations is constructed using adjoint representation and the invariants of associated Lie algebras of the system. Further, with the help of one-dimensional optimal system invariant solutions are constructed. Also, physically significant solutions such as traveling wave solutions, specifically the kink-type solitons and peakon-type solitons are obtained by using traveling wave transformations and all the solutions are graphically demonstrated. Finally, the hyperbolic nature of system of partial differential equations is examined by studying the evolutionary behavior of a discontinuity wave.

Suggested Citation

  • Karna, Ashutosh Kumar & Satapathy, Purnima, 2023. "Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011438
    DOI: 10.1016/j.chaos.2023.114241
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    References listed on IDEAS

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    1. Jana, Sumita & Kuila, Sahadeb, 2022. "Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Satapathy, Purnima & Raja Sekhar, T., 2018. "Optimal system, invariant solutions and evolution of weak discontinuity for isentropic drift flux model," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 107-116.
    4. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
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