光纤中暗孤子传输理论

THEORY OF DARK SOLITON PROPAGATIONIN OPTICAL FIBERS

本文基于引入的特定辅助谱参数ζ，避开了从原谱参数λ出发由于双值函数的出现不得不引入Ｒｉｅｍａｎｎ面造成的复杂，不仅简明地再导出了Ｚａｋｈａｒｏｖ和Ｓｈａｂａｔ关于ＮＬＳ方程在边值非０时求解的反散射方法，而且进一步导出了暗的多孤子解的显式，Ｊｏｓｔ解的完备集合与系统的Ｈａｍｉｌｔｏｎ理论。简单地解决了解的常数相引起的问题。最后，对含修正项的ＮＬＳ方程在边值非０时建立有效的微扰理论所遇到的困难进行了讨论。

To avoid complexity due to Riemann surface, required for doublevalued func-tion of the usual spectal parameter, starting from particular auxiliary parameter, the in-verse scattering equations of Zakharov-Shabat are rederived simply for the NLS equationwith nonvanishing boundary condition. In addition,explicit expressions of dark multi - soli-tion solutions, complete set of jost solution, and Hamiltonian formulism are also derived.The results obtained reach the same level as those for the NLS equation with v...