Vortex Ring Pinning for the Gross-Pitaevskii Equation in Three-Dimensional Space
Vortex Ring Pinning for the Gross-Pitaevskii Equation in Three-Dimensional Space
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DOI：
10.1137/110860379
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发表时间：
2012-11
期刊：
影响因子：
--
通讯作者：
Juncheng Wei;Jun Yang
中科院分区：
文献类型：
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作者：
Juncheng Wei;Jun Yang
We construct a stationary solution possessing two vortex rings to the nonlinear Schrodinger-type problem $ i u_t =-\varepsilon^2\triangle u +(V+|u|^2)u, $ where the unknown function $u$ is defined as $u:\mathbb {R}^3\times\mathbb{R}\rightarrow \mathbb{C}$, $\varepsilon$ is a small positive parameter, and $V$ is a real smooth potential. These two vortex rings will be pinned at a fixed site by the potential $V$. The two rings either lie in the same plane with neighboring interaction in the normal direction or they they lie in two parallel planes with interaction in the binormal direction, such that the neighboring interaction will be balanced by the effect of the potential.
