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2014 The nonlinear Schrödinger equation ground states on product spaces
Susanna Terracini, Nikolay Tzvetkov, Nicola Visciglia
Anal. PDE 7(1): 73-96 (2014). DOI: 10.2140/apde.2014.7.73

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.

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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

Information

Received: 2 May 2012; Accepted: 21 May 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1294.35148
MathSciNet: MR3219500
Digital Object Identifier: 10.2140/apde.2014.7.73

Subjects:
Primary: 35Q55
Secondary: 37K45

Keywords: Ground states , NLS , rigidity , stability , stability of solitons

Rights: Copyright © 2014 Mathematical Sciences Publishers

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