论文标题
$ 1D $ nls的孤立波的渐近稳定性具有吸引人的三角洲潜力
Asymptotic stability of solitary waves for the $1d$ NLS with an attractive delta potential
论文作者
论文摘要
我们考虑具有吸引人的三角势和质量质量非线性的一维非线性schrödinger方程。该方程式在聚焦和散焦病例中都接受了一个参数孤立的波浪解决方案家族。我们为满足合适光谱条件的所有孤立波建立了渐近稳定性，即，围绕孤立波周围的线性化操作员具有二维广义内核，没有其他特征值或共振。特别是，我们将先前的结果扩展到了小孤立波的状态，并扩展了福岛 - 奥塔 - 泽和kaminaga-ohta的结果，从轨道稳定到渐近稳定性。
We consider the one-dimensional nonlinear Schrödinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and defocusing cases. We establish asymptotic stability for all solitary waves satisfying a suitable spectral condition, namely, that the linearized operator around the solitary wave has a two-dimensional generalized kernel and no other eigenvalues or resonances. In particular, we extend our previous result beyond the regime of small solitary waves and extend the results of Fukuizumi-Ohta-Ozawa and Kaminaga-Ohta from orbital to asymptotic stability for a suitable family of solitary waves.
