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Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method

Author

Listed:
  • Remus-Daniel Ene

    (Department of Mathematics, Politehnica University of Timisoara, 2 Victoria Square, 300006 Timisoara, Romania
    These authors contributed equally to this work.)

  • Nicolina Pop

    (Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania
    These authors contributed equally to this work.)

  • Marioara Lapadat

    (Department of Mathematics, Politehnica University of Timisoara, 2 Victoria Square, 300006 Timisoara, Romania
    These authors contributed equally to this work.)

  • Luisa Dungan

    (Mech Machines Equipment & Transports Department, Politehnica University of Timisoara, 300222 Timisoara, Romania
    These authors contributed equally to this work.)

Abstract

This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the optimal homotopy asymptotic method (OHAM). These represent the ε -approximate OHAM solutions. A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure is suitable to be applied for dynamical systems with certain geometrical properties.

Suggested Citation

  • Remus-Daniel Ene & Nicolina Pop & Marioara Lapadat & Luisa Dungan, 2022. "Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method," Mathematics, MDPI, vol. 10(21), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4118-:d:963399
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    References listed on IDEAS

    as
    1. Cristian Lăzureanu & Tudor Bînzar, 2015. "On Some Properties and Symmetries of the 5-Dimensional Lorenz System," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, October.
    2. Cristian Lăzureanu & Tudor Bînzar, 2017. "Symmetries and Properties of the Energy-Casimir Mapping in the Ball-Plate Problem," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-13, January.
    3. Mădălina Sofia Paşca & Olivia Bundău & Adina Juratoni & Bogdan Căruntu, 2022. "The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    4. Constantin Bota & Bogdan Căruntu & Dumitru Ţucu & Marioara Lăpădat & Mădălina Sofia Paşca, 2020. "A Least Squares Differential Quadrature Method for a Class of Nonlinear Partial Differential Equations of Fractional Order," Mathematics, MDPI, vol. 8(8), pages 1-12, August.
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