Axial Symmetry of Normalized Solutions for Magnetic Gross-Pitaevskii Equations with Anharmonic Potentials
arXiv (Cornell University)(2023)
摘要
This paper is concerned with normalized solutions of the magnetic focusing Gross-Pitaevskii equations with anharmonic potentials in $\R^N$, where $N=2,3$. The existence of axially symmetric solutions is constructed as the parameter $a>0$ satisfies $a \to a_*(N)$, where $a_*(N)\geq0$ is a critical constant depending only on $N$. We further prove that up to the constant phase and rotational transformation, normalized concentrating solutions as $a\to a_*(N)$ must be unique and axially symmetric. As a byproduct, we also obtain that for the case $N=3$, the normalized concentrating solution as $a\to a_*(3)$ is free of vortices, where the anharmonic potential is non-radially symmetric.
更多查看译文
关键词
axial symmetry,normalized solutions,gross-pitaevskii
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要