摘 要：光纤中信息的传输存在衰减与色散的问题，采用了掺铒光纤放大器技术大大地抑制了光信号在光纤中的损耗。随着入纤功率的不断增大，色散问题成为限制波分复用的主要问题，针对光纤中光信息色散问题，从孤立水波能保持振幅与速度不变特性出发，提出了光脉冲在光纤中传递信息的方法，展开了高阶非线性薛定谔方程精确解的研究。对于含有四阶色散系数的非线性薛定谔方程，采用了具有复振幅的试探解，逐项计算，分离实部和虚部，再利用实部和虚部都为零，以及双曲正切函数幂指数系数为零，得到了一系列方程，从而获得四阶色散系数非线性薛定谔方程的精确解。根据试探解的形式不同，得到了暗孤子解和亮孤子解。进而 采用含有双曲正割平方项的新型孤子试探解，得到了非常复杂的11个方程，最后还是回到了暗孤子解。结果表明，采用具有复振幅的试探解法，再进行分离实部和虚部等方法，能够得到高阶非线性薛定谔方程的精确解，从而为光脉冲在光纤中传递信息提供了理论依据。
关键词：信息光学，非线性薛定谔方程，四阶色散，孤子解
Abstract：For the problems of attenuation and dispersion in optical fiber transmission, there are many methods had been put forward. One of them the technology of Erbium-doped fiber amplifier had suppressed the loss of the light signal in the optical fiber. With increasing of the input power, the dispersion problem had been become restricted problem for WDM. For the problem, a series schemes had been proposed. One of the schemes was that the optical pulse transmitted in optical fiber based on the isolated water wave. The character of the isolated water wave was that the amplitude and the speed kept as same as original amplitude and speed. The character was discovered by James Scott Russell in 1834. The study of the exact solution in high order nonlinear Schrödinger equation had been developed. The research was based on the four order dispersion. The method was that the trial solution was plane wave function with complex amplitude. After the each items of the nonlinear Schrödinger equation with the four order dispersion calculated, the real part and the imaginary part had been separated and they were zero, respectively. A series of equations had been got when the coefficients of the hyperbolic tangent function with various exponential were zero. The exact solution in nonlinear Schrödinger equation with four order dispersion obtained. The exact solutions had concluded dark solitonary solution and the bright solitonary solution based on various forms of the trial solution. The complex trial solution with hyperbolic secant square function had been finished in nonlinear Schrödinger equation with four order dispersion. The complex 11 equations had obtained based on the two conditions. The first one was that the real part and the imaginary part had been separated and they were zero, respectively. The second one was that the coefficients of the hyperbolic tangent function with various exponential were zero. The finally result was back to the dark solitonary solution. The results show that the method was very good. The method had three steps. The first step was that the trial solution with complex amplitude was assumed. The second step was that the real part and the imaginary part had been separated and they were zero, respectively. The third step was that the coefficients of the hyperbolic tangent function with various exponential were zero. The exact solutions had got after three steps. The results provided a theoretical basis for the optical pulse in optical fiber transmission.
Key words: Information Optics; nonlinear Schrödinger equation; four order dispersion; solitonary solution
