论文标题
在非线性schrödinger方程式上，在强限制方面具有环形陷阱
On the nonlinear Schrödinger equation with a toroidal trap in the strong confinement regime
论文作者
论文摘要
我们考虑具有强弹圈的3D立方非线性schrödinger方程（NLS）。在第一部分中，我们表明，随着限制的加强，可以通过求解1D周期性NLS（定理1.4）的一类时间依赖模型的一类全局解决方案。在第二部分中，我们将稳态构建为受约束的能量最小化器，并证明其尺寸还原为众所周知的1d周期基态（定理1.6和1.7）。然后，使用降低限制，我们建立了3D环Soliton（定理1.8）的局部唯一性和轨道稳定性。这些结果证明了物理实验中的环上的玻色子凝结物的稳定准1D周期动力学的出现是合理的。
We consider the 3D cubic nonlinear Schrödinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of global solutions to the time-dependent model can be described by 1D flows solving the 1D periodic NLS (Theorem 1.4). In the second part, we construct a steady state as a constrained energy minimizer, and prove its dimension reduction to the well-known 1D periodic ground state (Theorem 1.6 and 1.7). Then, employing the dimension reduction limit, we establish the local uniqueness and the orbital stability of the 3D ring soliton (Theorem 1.8). These results justify the emergence of stable quasi-1D periodic dynamics for Bose-Einstein condensates on a ring in physics experiments.
