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On group analysis of the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov equation in quantum magneto-plasmas

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  • Liu, Jian-Gen
  • Yang, Xiao-Jun
  • Feng, Yi-Ying
  • Cui, Ping

Abstract

In this article, the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov (Z–K) equation in quantum magneto-plasmas, is executed. First of all, the symmetry of this considered equation by using group analysis approach with the sense of Riemann–Liouville (R–L) fractional derivative, is obtained. Then, the symmetry of the above yielded, the optimal system of one-dimensional subalgebras for this equation is also found. Subsequently, the original equation can be reduced into (1+1)-dimensional fractional differential equation with the adding of extended Erdélyi–Kober fractional differential operator. Further, the one parameter group, invariant solutions and non-invariant solutions are constructed. Finally, the conservation laws are also shown with a new conservation theorem. We believe that these beautiful results can help us to discover more evolutionary mechanisms of the considered equation.

Suggested Citation

  • Liu, Jian-Gen & Yang, Xiao-Jun & Feng, Yi-Ying & Cui, Ping, 2020. "On group analysis of the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov equation in quantum magneto-plasmas," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 407-421.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:407-421
    DOI: 10.1016/j.matcom.2020.07.005
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    References listed on IDEAS

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    1. Huang, Qing & Zhdanov, Renat, 2014. "Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 110-118.
    2. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
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    Cited by:

    1. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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