The NLS ground states on product spaces

Susanna Terracini; Nikolay Tzvetkov; Nicola Visciglia

doi:10.2140/apde.2014.7.73

The NLS ground states on product spaces

Analysis of PDEs 2016-01-20 v1

Authors: Susanna Terracini , Nikolay Tzvetkov , Nicola Visciglia

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Abstract

We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$ , where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the ground states coincide with the corresponding $\R^n$ ground states. We also prove that above a critical mass the ground states have nontrivial $M^k$ dependence. Finally, we address the Cauchy problem issue which transform the variational analysis to dynamical stability results.

Keywords

nonlinear Schr\"odinger equation ground states product spaces compact Riemannian manifold critical mass Cauchy problem dynamical stability

Cite

@article{arxiv.1205.0342,
  title  = {The NLS ground states on product spaces},
  author = {Susanna Terracini and Nikolay Tzvetkov and Nicola Visciglia},
  journal= {arXiv preprint arXiv:1205.0342},
  year   = {2016}
}

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24 pages

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