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Some qualitative studies of the focusing inhomogeneous Gross–Pitaevskii equation
Zeitschrift für angewandte Mathematik und Physik ( IF 2 ) Pub Date : 2020-04-24 , DOI: 10.1007/s00033-020-01301-z Alex H. Ardila , Van Duong Dinh
中文翻译:
关于聚焦非均匀Gross–Pitaevskii方程的定性研究
更新日期:2020-04-24
Zeitschrift für angewandte Mathematik und Physik ( IF 2 ) Pub Date : 2020-04-24 , DOI: 10.1007/s00033-020-01301-z Alex H. Ardila , Van Duong Dinh
We study the Cauchy problem for an inhomogeneous Gross–Pitaevskii equation. We first derive a sharp threshold for global existence and blowup of the solution. Then, we construct and classify finite time blowup solutions at the minimal mass threshold. Additionally, using variational techniques, we study the existence, the orbital stability and instability of standing waves.
中文翻译:
关于聚焦非均匀Gross–Pitaevskii方程的定性研究
我们研究了一个不均匀的Gross–Pitaevskii方程的柯西问题。我们首先得出全球存在和解决方案爆炸的严格门槛。然后,我们以最小质量阈值构造和分类有限时间爆燃解决方案。此外,我们使用变分技术研究了驻波的存在,轨道稳定性和不稳定性。