光纤非线性Schrdinger方程新的解析解

New analytic solutions of nonlinear Schrodinger equation for optic fiber

把广义椭圆函数法和形变映射法相结合,借助Mathematica软件,构建了光纤变系数非线性薛定谔方程的一大类新的孤子解析解,讨论了无啁啾情形的孤子解.除了得到包括亮、暗孤子解和类孤子解在内的一些已知的精确解外,还得到了许多Jacobi类椭圆函数形式的新解,这些解在极限情形下会退化为类孤立波解及类三角函数解,同时对基本孤子的色散控制方法进行了讨论.结果表明:光纤信号的多个指标都可以通过二阶色散项系数进行控制.作为特例,讨论了周期增益或损耗光纤系统的包络型孤子解,得到了有意义的结果.

Based on extended Jacobi elliptic functions expansion method and mapping expansion method, the variable coefficient nonlinear Schrodinger equation for optic fiber was investigated by the general mapping expansion method. With the aid of Mathematica software, plenty of new soliton analytical solutions were obtained to discuss the soliton solutions under non-chirp case. Besides many known solutions of bright dark and soliton-like solutions, some new Jacobi-like elliptic function solutions were obtained which were generated to soliton-like solutions and single triangle-like function solutions in limit cases. The dispersion managed method for the basic soliton solution was also discussed. The results show that many index of the optical signal can be controlled by the coefficient of second order dispersion term. The envelope soliton solutions of optical fiber system with periodic gain or loss were discussed with many meaningful results.