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• W3178606411 abstract "We consider the 3d cubic nonlinear Schrodinger equation (NLS) with a strong 2d harmonic potential. The model is physically relevant to observe the lower-dimensional dynamics of the Bose-Einstein condensate, but its ground state cannot be constructed by the standard method due to its supercritical nature. In Bellazzini-Boussaid-Jeanjean-Visciglia cite{BBJV}, the authors constructed a proper ground state introducing a constrained energy minimization problem. In this paper, we further investigate the properties of the ground state. First, we show that as the partial confinement is increased, the 1d ground state is derived from the 3d energy minimizer with a precise rate of convergence. Then, by employing this dimension reduction limit, we prove the uniqueness of the 3d minimizer provided that the confinement is sufficiently strong. Consequently, we obtain the orbital stability of the minimizer, which improves that of the set of minimizers in the previous work cite{BBJV}." @default.
• W3178606411 created "2021-07-19" @default.
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• W3178606411 date "2021-07-12" @default.
• W3178606411 modified "2023-10-14" @default.
• W3178606411 title "Uniqueness and orbital stability of standing waves for the nonlinear Schrodinger equation with a partial confinement" @default.
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• W3178606411 doi "https://doi.org/10.48550/arxiv.2107.05185" @default.
• W3178606411 hasPublicationYear "2021" @default.
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