Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupledHirota–Maxwell–Bloch equations

Abstract

We propose the system of generalized inhomogeneous coupled Hirota–Maxwell–Blochequations which describes propagation of an optical soliton in an inhomogeneouserbium-doped fiber with two-level resonant atoms. For this system, higher-order dispersion,self-steepening and self-Raman scattering are assumed to be inhomogeneous, like the groupvelocity dispersion. The exact analytical multisoliton solutions are obtained byemploying the simple, straightforward Darboux transformation based on the obtained3 × 3 Lax pair. As an example, the one- and two-soliton solutions in explicit forms are generated.Then, we give the relative numerical evolution and discuss the propagation characteristicsof the pulse.