Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 26 September 2022 / Approved: 30 September 2022 / Online: 30 September 2022 (03:52:42 CEST)

How to cite: Ene, R.; Pop, N.; Lapadat, M.; Dungan, L. Approximate Closed-form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method. Preprints 2022, 2022090474. https://doi.org/10.20944/preprints202209.0474.v1 Ene, R.; Pop, N.; Lapadat, M.; Dungan, L. Approximate Closed-form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method. Preprints 2022, 2022090474. https://doi.org/10.20944/preprints202209.0474.v1

Abstract

This work 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). 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 could be successfully applied for more dynamical systems with geometrical properties.

Keywords

optimal homotopy asymptotic method; Maxwell--Bloch equations; symmetries; Hamilton--Poisson realization; periodical orbits

Subject

Computer Science and Mathematics, Computational Mathematics

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