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arXiv · 2103.16353

On orbital stability of the physical ground states of the NLS equations

Yavdat Il'yasov
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Abstract

We prove orbital stability result for physical ground states of a nonlinear Schr\"{o}dinger (NLS) equation in the sense that the set of these ground states is contained in the set of prescribed mass solutions which is orbital stable by the Cazenave-Lions theorem. We apply the nonlinear generalized Rayleigh quotients method which allows establishing a one-to-one correspondence between the values of the mass $m$, the frequency $\lambda$, and the action level $S$ of the physical ground states.

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Yavdat Il'yasov. 2021-03-30. On orbital stability of the physical ground states of the NLS equations. https://arxiv.org/abs/2103.16353

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