This paper concerns the nonlinear Schrödinger equation which describes the dipolar quantum gases. When the energy plus mass is lower than the mass of the ground state, we find we can use the kinetic energy and mass of the initial data to divide the subspace into two parts. If the initial data are in one of the parts, the solutions exist globally. Moreover, by using the Kening-Merle roadmap method, we find that these solutions will scatter. If initial data are in the other part, the solutions will collapse. And hence, the standing waves are strong unstable.

中文翻译：

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偶极子量子气体驻波的散射和强烈不稳定性

本文涉及描述双极量子气体的非线性Schrödinger方程。当能量加质量低于基态的质量时，我们发现可以使用动能和初始数据的质量将子空间分为两部分。如果初始数据在其中一部分中，则解决方案全局存在。此外，通过使用Kening-Merle路线图方法，我们发现这些解决方案将分散。如果其他部分包含初始数据，则解决方案将崩溃​​。因此，驻波很不稳定。