聚焦非线性薛定谔方程椭圆解的轨道稳定性
The orbital stability of elliptic solutions of the Focusing Nonlinear Schrödinger Equation
摘要：
研究了聚焦非线性薛定谔方程（NLS）椭圆解在次谐扰动下的稳定性。利用NLS的可积性，我们讨论了椭圆解的谱稳定性，建立了较小振幅的解相对于较大的扰动类是稳定的。我们表明，光谱稳定的解决方案是轨道稳定的构造一个李雅普诺夫功能使用高阶守恒量的NLS。
英文摘要：
We examine the stability of the elliptic solutions of the focusing nonlinear Schrödinger equation (NLS) with respect to subharmonic perturbations. Using the integrability of NLS, we discuss the spectral stability of the elliptic solutions, establishing that solutions of smaller amplitude are stable with respect to larger classes of perturbations. We show that spectrally stable solutions are orbitally stable by constructing a Lyapunov functional using higher-order conserved quantities of NLS.
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