Analysis & PDE

The nonlinear Schrödinger equation ground states on product spaces

Susanna Terracini, Nikolay Tzvetkov, and Nicola Visciglia

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731466

Digital Object Identifier
doi:10.2140/apde.2014.7.73

Mathematical Reviews number (MathSciNet)
MR3219500

Zentralblatt MATH identifier
1294.35148

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

Keywords
NLS stability stability of solitons rigidity ground states

Citation

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. https://projecteuclid.org/euclid.apde/1513731466


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