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

Remus-Daniel Ene, Nicolina Pop (), Marioara Lapadat and Luisa Dungan
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Remus-Daniel Ene: Department of Mathematics, Politehnica University of Timisoara, 2 Victoria Square, 300006 Timisoara, Romania
Nicolina Pop: Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania
Marioara Lapadat: Department of Mathematics, Politehnica University of Timisoara, 2 Victoria Square, 300006 Timisoara, Romania
Luisa Dungan: Mech Machines Equipment & Transports Department, Politehnica University of Timisoara, 300222 Timisoara, Romania

Mathematics, 2022, vol. 10, issue 21, 1-13

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.

Keywords: Maxwell–Bloch equations; Hamilton–Poisson realization; periodical orbits; symmetries; optimal homotopy asymptotic method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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