论文标题
非线性schrödinger方程的驻波的存在和稳定性具有关键的旋转速度
Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed
论文作者
论文摘要
我们研究了与cauchy问题相关的常势的存在和稳定性，该非线性schrödinger方程（NLS）具有临界旋转速度和轴向对称的谐波电位。该方程是作为一个有效模型，描述了具有角速度旋转的磁陷阱中有吸引力的玻色网凝结。通过将方程式视为具有恒定磁场的NLS，并具有（或不具有）部分谐波限制，我们确定了规定的质量站立波的存在和轨道稳定性，用于具有质量 - 批判性，质量批判性和质量性非线性的方程式。我们的结果扩展了[Bellazzini-Boussaïd-Jeanjean-Visciglia，Comm。数学。物理。 353（2017），没有。 1，229-251]，在其中建立了具有部分限制的超临界NLS的站立波的存在和稳定性。
We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schrödinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an effective model describing the attractive Bose-Einstein condensation in a magnetic trap rotating with an angular velocity. By viewing the equation as NLS with a constant magnetic field and with (or without) a partial harmonic confinement, we establish the existence and orbital stability of prescribed mass standing waves for the equation with mass-subcritical, mass-critical, and mass-supercritical nonlinearities. Our result extends a recent work of [Bellazzini-Boussaïd-Jeanjean-Visciglia, Comm. Math. Phys. 353 (2017), no. 1, 229-251], where the existence and stability of standing waves for the supercritical NLS with a partial confinement were established.
