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Lie Symmetry Classification and Qualitative Analysis for the Fourth-Order Schrödinger Equation

Author

Listed:
  • Andronikos Paliathanasis

    (Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa
    Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia 5090000, Chile)

  • Genly Leon

    (Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa
    Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1240000, Chile)

  • Peter G. L. Leach

    (Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa)

Abstract

The Lie symmetry analysis for the study of a 1 + n fourth-order Schrödinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential function where non-trivial Lie symmetries exist and simplify the Schrödinger equation. Then, a qualitative analysis allows for the reduced ordinary differential equation to be analysed to understand the asymptotic dynamics.

Suggested Citation

  • Andronikos Paliathanasis & Genly Leon & Peter G. L. Leach, 2022. "Lie Symmetry Classification and Qualitative Analysis for the Fourth-Order Schrödinger Equation," Mathematics, MDPI, vol. 10(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3204-:d:906868
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    References listed on IDEAS

    as
    1. Sajid Ali & M. Safdar & Asghar Qadir, 2014. "Linearization from Complex Lie Point Transformations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, November.
    2. Zhang, Zhi-Yong & Li, Guo-Fang, 2020. "Lie symmetry analysis and exact solutions of the time-fractional biological population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. S. Jamal & A. H. Kara & R Narain, 2012. "Wave Equations in Bianchi Space-Times," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, December.
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