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On Lie symmetries, optimal systems and explicit solutions to the Kudryashov–Sinelshchikov equation

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  • Tu, Jian-Min
  • Tian, Shou-Fu
  • Xu, Mei-Juan
  • Zhang, Tian-Tian

Abstract

Under investigation in this paper is the Kudryashov–Sinelshchikov equation, which describes influence of viscosity and heat transfer on propagation of the pressure waves. The Lie symmetry method is used to study its vector fields and optimal systems, respectively. Furthermore, the symmetry reductions and exact solutions of the equation are obtained on the basic of the optimal systems. Finally, based on the power series theory, a kind of explicit power series solutions for the equation is well constructed with a detailed derivation.

Suggested Citation

  • Tu, Jian-Min & Tian, Shou-Fu & Xu, Mei-Juan & Zhang, Tian-Tian, 2016. "On Lie symmetries, optimal systems and explicit solutions to the Kudryashov–Sinelshchikov equation," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 345-352.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:345-352
    DOI: 10.1016/j.amc.2015.11.072
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    References listed on IDEAS

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    1. Ivanova, N.M. & Popovych, R.O. & Sophocleous, C. & Vaneeva, O.O., 2009. "Conservation laws and hierarchies of potential symmetries for certain diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 343-356.
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    Cited by:

    1. Wang, Xiu-Bin & Tian, Shou-Fu & Xua, Mei-Juan & Zhang, Tian-Tian, 2016. "On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 216-233.
    2. Sarah M. Albalawi & Adel A. Elmandouh & Mohammed Sobhy, 2024. "Integrability and Dynamic Behavior of a Piezoelectro-Magnetic Circular Rod," Mathematics, MDPI, vol. 12(2), pages 1-16, January.
    3. Adel Elmandouh & Aqilah Aljuaidan & Mamdouh Elbrolosy, 2024. "The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation," Mathematics, MDPI, vol. 12(3), pages 1-15, January.

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