论文标题
浓缩NLSE的站立波的稳定性在两个方面
Stability of the standing waves of the concentrated NLSE in dimension two
论文作者
论文摘要
在本文中，我们将继续对固定的，点，非线性的二维schrödinger方程进行分析[2，13]。在该模型中，爆炸现象的发生具有两个特征：所有溶液吹来的能量阈值严格呈负面，并且与站立波的最大能量相吻合；没有关键的力量非线性，即，对于每个力量都有爆炸解决方案。在这里，我们研究了固定状态的稳定性，以验证前面提到的异常是否具有稳定性特征的对应物。
In this paper we will continue the analysis of two dimensional Schrödinger equation with a fixed, pointwise, nonlinearity started in [2, 13]. In this model, the occurrence of a blow-up phenomenon has two peculiar features: the energy threshold under which all solutions blow up is strictly negative and coincides with the infimum of the energy of the standing waves; there is no critical power nonlinearity, i.e., for every power there exist blow-up solutions. Here we study the stability properties of stationary states to verify whether the anomalies mentioned before have any counterpart on the stability features.
