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Z. Naturforsch. 66a, 712 – 720 (2011)
doi:10.5560/ZNA.2011-0035
Multi-Soliton Solutions for an Inhomogeneous Nonlinear Schrödinger–Maxwell–Bloch System in the Erbium-Doped Fiber
Ming Wang, Wen-Rui Shan, Xing Lü, Bo Qin, and Li-Cai Liu
School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China
Received March 3, 2011 / revised June 30, 2011
Reprint requests to: W.-R. S.; E-mail: shanwenrui@sina.com
Under investigation in this paper is an inhomogeneous nonlinear Schrödinger–Maxwell–Bloch system with variable dispersion and nonlinear effects, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Hirota method and symbolic computation. Evolution and interaction of the solitons are plotted, and the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. Overall phase shift can be observed when the parameter accounting for the interaction between the silica and doped erbium atoms is taken as a constant.
Key words: Erbium-Doped Fiber; Inhomogeneous Nonlinear Schrödinger-Maxwell-Bloch System; Evolution and Interaction of Solitons; Multi-Soliton Solutions; Symbolic Computation.
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