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Lie Symmetry Group, Invariant Subspace, and Conservation Law for the Time-Fractional Derivative Nonlinear Schrödinger Equation

Author

Listed:
  • Fan Qin

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Wei Feng

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Songlin Zhao

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

Abstract

In this paper, a time-fractional derivative nonlinear Schrödinger equation involving the Riemann–Liouville fractional derivative is investigated. We first perform a Lie symmetry analysis of this equation, and then derive the reduced equations under the admitted optimal-symmetry system. Moreover, with the invariant subspace method, several exact solutions for the equation and their figures are presented. Finally, the new conservation theorem is applied to construct the conservation laws of the equation.

Suggested Citation

  • Fan Qin & Wei Feng & Songlin Zhao, 2022. "Lie Symmetry Group, Invariant Subspace, and Conservation Law for the Time-Fractional Derivative Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2170-:d:844840
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    References listed on IDEAS

    as
    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. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 371-383.
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