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Exact Solutions for a Modified Schrödinger Equation

Author

Listed:
  • Yassine Benia

    (Department of Mathematics and Informatics, University of Benyoucef Benkhedda (Alger 1), Algiers 16000, Algeria)

  • Marianna Ruggieri

    (Faculty of Engineering and Architecture, University of Enna “Kore”, 94100 Enna, Italy)

  • Andrea Scapellato

    (Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy)

Abstract

The aim of this paper was to propose a systematic study of a ( 1 + 1 ) -dimensional higher order nonlinear Schrödinger equation, arising in two different contexts regarding the biological science and the nonlinear optics. We performed a Lie symmetry analysis and here present exact solutions of the equation.

Suggested Citation

  • Yassine Benia & Marianna Ruggieri & Andrea Scapellato, 2019. "Exact Solutions for a Modified Schrödinger Equation," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:908-:d:271922
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    References listed on IDEAS

    as
    1. Daniel, M. & Latha, M.M., 2001. "A generalized Davydov soliton model for energy transfer in alpha helical proteins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 351-370.
    2. Georgiev, Danko D. & Glazebrook, James F., 2019. "Quantum tunneling of Davydov solitons through massive barriers," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 275-293.
    3. Georgiev, Danko D. & Glazebrook, James F., 2019. "On the quantum dynamics of Davydov solitons in protein α-helices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 257-269.
    4. Galane J. Luo & Bernard M. A. G. Piette, 2017. "A generalised Davydov-Scott model for polarons in linear peptide chains," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(8), pages 1-21, August.
    5. Cisneros-Ake, Luis A. & Brizhik, L., 2019. "Charge and energy transport by Holstein solitons in anharmonic one-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 343-354.
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    Cited by:

    1. József Abaffy & Szabina Fodor, 2021. "ABS-Based Direct Method for Solving Complex Systems of Linear Equations," Mathematics, MDPI, vol. 9(19), pages 1-17, October.
    2. Karim Guida & Khalid Hilal & Lahcen Ibnelazyz, 2020. "Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    3. Xuemei Li & Lutong Li, 2020. "On Construction of a Super Hierarchy of the Wadati‐Konno‐Ichikawa Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).

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