标题： 时间依赖势中的孤立波动力学 显示英文标题

标题： Solitary wave dynamics in time-dependent potentials

摘要： 我们严格研究非线性薛定谔方程在{\it 时间依赖的}外部势中的孤子解的长时间动力学。 为了奠定基础，我们首先建立了广义非自治非线性薛定谔方程的柯西问题的适定性。 然后我们表明，在外部势相对于孤子尺寸在空间上缓慢变化的{\it 空间绝热}情况下，孤子中心的动力学由哈密顿方程描述，加上辐射阻尼产生的项。 最后我们对我们的分析的两个物理应用进行说明。 第一个是孤子的绝热传输，第二个是由于时间周期性扰动导致的被束缚孤子的马蒂厄不稳定性。 显示英文摘要

摘要： We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schr\"odinger equation. We then show that in the {\it space-adiabatic} regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. We finally remark on two physical applications of our analysis. The first is adiabatic transportation of solitons, and the second is Mathieu instability of trapped solitons due to time-periodic perturbations.