Submitted:
26 September 2022
Posted:
30 September 2022
You are already at the latest version
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
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