两类非线性薛定谔方程的调制不稳定性

The modulation instability of two kinds of nonlinear Schr?dinger equations

调制不稳定性在诸多科学领域作为解释一些物理现象起到非常重要的作用,比如在非线性光纤光学中常用它解释和控制由非线性项与色散项相互作用产生的非线性波的不稳定性,在研究海洋怪波产生的机制中它为怪波产生提供了一定的依据,光纤通信中调制不稳定性在色散管理孤子中得到很好的应用.本文基于两类典型的非线性薛定谔方程,分析了平面波的调制不稳定性区域,给出在特定参数及不同振幅条件下的增益谱图像.

Modulation instability plays a supporting role to explain some phenomena in many fields as a basic theory , such as nonlinear optical light w hich use it to explain and control the instability originate the interaction between the nonlinear term and dispersion parts . Instead of finding the mechanism of rogue wave＇s foundation , it is the modulation instability plays an important reason . In optical fiber communication modulation instability obtained the very good application in the dispersion management solitons .In this paper we start form two classes of nonlinear Schr？dinger equation and analyze their instability region , at the same time we give the gain spectrum graphics under the condition that with specific parameters and different amplitudes .