摘 要：在光纤通信中衰减和色散是两大难题，随着掺铒光纤放大器的诞生并使用，有效地解决了衰减问题，随着入纤光功率的增大，色散问题严重地限制了波分复用，借助于孤子在运动过程中其形状和速度能保持不变的特性，超短脉冲在光纤中传输可望有效地解决色散问题。针对非线性光纤中超短脉冲传输满足的是高阶非线性薛定谔方程，采用了G'/G 展开法，进行精确求解。首先采用G'/G 展开法对DSW方程进行精确求解，得到了G'/G展开法求解方程的一般方法。然后针对非线性光纤中超短脉冲传输，存在着群速度色散、自相位调制等满足的具有四阶色散项和五次非线性项的高阶非线性薛定谔方程，进行精确求解，得到了扭结型孤波解、反扭结型孤波解、正切三角函数型孤波解、余切三角函数型孤波解。结果表明，作为一种新型的解法G'/G 展开法对于非线性光纤中超短脉冲传输的高阶非线性薛定谔方程，能得到精确的孤子解，为超短脉冲在光纤中传输提供理论依据。
关键词：信息光学，光纤，非线性薛定谔方程，展开法
Abstract：There are two major problems in the optical fiber communication. The first one is the attenuation. Another is the dispersion. The attenuation problem had been effectively controlled with the development of erbium doped fiber amplifier (EDFA). With increasing of optical power in fiber the dispersion problem had restricted severely the wavelength division multiplexing (WDM). The characteristics of the soliton would help the ultrashort pulse in optical fiber transmission. The characteristics are the shape and the speed could keep constant when the soliton was moving in the process. The ultrashort pulse in optical fiber transmission was expected to control effectively dispersion. The propagation of the nonlinear ultra-short laser pulse in fibers which fits the high order nonlinear Schrödinger equation had been solved exactly with the G'/G expansion method. The general scheme of the G'/G expansion method was found by exact solution for the DSW equation. Then the problems of the nonlinear fiber ultra-short pulse transmission had been solved exactly with the G'/G expansion method. The problems concluded the group velocity dispersion, the self phase modulation, and so on. The problems fit for the high order nonlinear Schrödinger equation with the items of the four order dispersion and the power of five nonlinear. A series of solutions had been obtained such as the solitary wave solutions of kink, inverse kink, tangent trigonometric function, and co tangent trigonometric function. The results shown that the G'/G expansion method was effective method in solving exactly for the high order nonlinear Schrödinger equation. The propagation of the nonlinear ultra-short laser pulse in fibers fit the high order nonlinear Schrödinger equation. The exact solitary wave solution had been got. The result provided a theoretical basis for the transmission of the ultra-short pulse in nonlinear optical fiber.
Key words: Information optics, optics fiber, nonlinear Schrödinger equation, G'/G expansion method
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