具波动算子非线性Schrodinger方程行波解的稳定性

研究具有波动算子的非线性Schrodinger方程的行波解的存在性、不稳定性与色散关系。通过给出该方程Stokes解，在振幅和相位上引入小扰动，来分析行波解的线性稳定性；利用一元四次方程的拉格朗日解法并结合盛金公式对含参数四次方程解的分布情况进行讨论，给出了参数α、β、振幅u0与波数q之间的关系,得到行波解的振荡性、稳定性及不稳定的条件和色散关系。

Stability of the Traveling Wave Solutions About the Nonlinear Schrodinger Equation with Wave Operator

The existence,stability and dispersion of traveling wave solutions about the nonlinear Schrodinger equation with wave operator were discussed.By giving the Stokes solution of the equation,the small perturbations were introduced into the amplitude and phase to analyze the linear stability of the traveling wave solutions.As the same time,using a quartic equation of Lagrange method and combining with Shengjin＇s formula on distribution with parameter quartic equation solution were discussed,and the relation between the parameters α,β,the amplitude u0 and the wave number q was given,and the oscillation,the stability and the unstable condition and the dispersion relation of the traveling wave solutions were obtained.