非线性薛定谔方程的稳态解及其稳定性研究

Steady Solution and Its Stability of Nonlinear Schr(o)dinger Equation

用行波变换方法和分叉理论研究里非线性薛定谔方程的定常解和定常解的稳定性，计算结果表明：非线性薛定谔方程存在两类定常解，静态解和平面波解，对于具有正阻尼和软特性的非线性薛定谔方程，稳定的平面解存在于正常色散媒质中，而对于具有正阻尼和硬特性的非线性薛定谔方程，稳态平面波解只存在于反常色散媒质中，此外，非线性薛定谔方程在行波变换下的派生系统在处发生Hopf分叉。

The steady solution and its stability of Nonlinear Schrdinger Equation(NLSE) are studied by means of traveling wave transformation and bifurcation theory. There are two types of steady solution: zero solution and planar wave solution. If damping is positive and nonlinear is softening, the stable planar wave solution of NLSE exists in normal dispersive medium, and if nonlinear is hardening, the stable planar wave solution of NLSE exists in abnormal dispersive medium.