We study the nature of the nonlinear Schrödinger equation ground states on the product spaces Rn × Mk , where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding ℝn ground states. We also prove that above a critical mass the ground states have nontrivial Mk dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.
The nonlinear Schrödinger equation ground states on product spaces
TERRACINI, Susanna;
2014-01-01
Abstract
We study the nature of the nonlinear Schrödinger equation ground states on the product spaces Rn × Mk , where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding ℝn ground states. We also prove that above a critical mass the ground states have nontrivial Mk dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.
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