Optical soliton propagation in an erbium doped nonlinear light guide with higher order dispersion

We propose a coupled system of the Hirota equation and the Maxwell-Bloch equations to describe the wave propagation in an erbium doped nonlinear fiber with higher order dispersion. The Painlevé property of the same is analyzed and the coupled system is found to be integrable. The Lax pair is also constructed and the single-soliton solution is explicitly shown. The coupled system is found to allow soliton-type propagation