In this paper, we consider the NLS equation with focusing nonlinearities in the presence of a potential. We investigate the compact soliton motions that correspond to a free soliton escaping the well created by the potential. We exhibit the dynamical system driving the exiting trajectory and construct associated nonlinear dynamics for untrapped motions. We show that the nature of the potential/soliton is fundamental, and two regimes may exist: one where the tail of the potential is fat and dictates the motion, and one where the tail is weak and the soliton self-interacts with the potential defects, hence leading to different motions.

中文翻译：

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逃逸势阱的非线性薛定ding方程的行波

在本文中，我们考虑存在电位时具有聚焦非线性的NLS方程。我们研究了紧凑的孤子运动，这些运动对应于逃逸由势所产生的井的自由孤子。我们展示了驱动现有轨迹的动力学系统，并为未捕获的运动构造了关联的非线性动力学。我们证明了电势/孤子的本质是基本的，可能存在两种状态：一种电势的尾巴是脂肪并决定运动；一种电势的尾巴是弱的并且孤子与电势缺陷自相互作用，因此导致不同的动作。