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Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations

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  • Sahoo, S.
  • Ray, S. Saha

Abstract

In this paper, the invariance properties of time fractional coupled Drinfeld–Sokolov–Satsuma–Hirota (DSSH) equations have been investigated using the Lie group analysis method. In this regard a systematic research to derive Lie point symmetries of time fractional coupled DSSH equations is performed. Using the Lie group analysis method, the vector fields and the symmetry reduction of the time fractional coupled DSSH equations are obtained. It is shown that, the time fractional coupled DSSH equations can be reduced to the fractional coupled ordinary differential equations by using fractional Erdélyi–Kober differential operator with Riemann–Liouville derivative. Finally using new conservation theorem with formal Lagrangian, the new conserved vectors are well constructed with a detailed derivation, which present the conservation analysis for time fractional coupled Drinfeld–Sokolov–Satsuma–Hirota (DSSH) equations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:725-733
    DOI: 10.1016/j.chaos.2017.09.031
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    References listed on IDEAS

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    1. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time-Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, January.
    2. 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.
    3. Ahmet Bekir & Özkan Güner & Adem C. Cevikel, 2013. "Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, June.
    4. Abdon Atangana & Dumitru Baleanu, 2013. "Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
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    Cited by:

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    2. Zehra Pinar Izgi & Pshtiwan Othman Mohammed & Ravi P. Agarwal & Majeed A. Yousif & Alina Alb Lupas & Mohamed Abdelwahed, 2024. "Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis," Mathematics, MDPI, vol. 12(18), pages 1-9, September.
    3. 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.
    4. 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).

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