Abstract
We study the nature of the nonlinear Schrödinger equation ground states on the product spaces , where is a compact Riemannian manifold. We prove that for small masses the ground states coincide with the corresponding ground states. We also prove that above a critical mass the ground states have nontrivial dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.
Citation
Susanna Terracini. Nikolay Tzvetkov. Nicola Visciglia. "The nonlinear Schrödinger equation ground states on product spaces." Anal. PDE 7 (1) 73 - 96, 2014. https://doi.org/10.2140/apde.2014.7.73
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