Analysis & PDE

The nonlinear Schrödinger equation ground states on product spaces

Susanna Terracini, Nikolay Tzvetkov, and Nicola Visciglia

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We study the nature of the nonlinear Schrödinger equation ground states on the product spaces n×Mk, where Mk is a compact Riemannian manifold. We prove that for small L2 masses the ground states coincide with the corresponding n 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.

Article information

Anal. PDE, Volume 7, Number 1 (2014), 73-96.

Received: 2 May 2012
Accepted: 21 May 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 37K45: Stability problems

NLS stability stability of solitons rigidity ground states


Terracini, Susanna; Tzvetkov, Nikolay; Visciglia, Nicola. The nonlinear Schrödinger equation ground states on product spaces. Anal. PDE 7 (2014), no. 1, 73--96. doi:10.2140/apde.2014.7.73.

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