Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space

Abstract

We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.

New: As noted in Banica-Duyckaerts (arXiv:1411.0846), Section 5 should read that for sufficiently large mass, sub-critical problems can be solved via energy minimization for all d \geq 2 and as a result Cazenave-Lions results can be applied in Section 6 with the same restriction. These requirements were addressed by the subsequent work with Metcalfe and Taylor in arXiv:1203.3612

References in corpus (3)

• Nonlinear Schrödinger equation on real hyperbolic spaces
• On scattering for NLS: from Euclidean to hyperbolic space
• Semilinear Schrödinger Flows on Hyperbolic Spaces: Scattering in H^1

Cited by in corpus (6)

• Dispersive Estimates for Scalar and Matrix Schrödinger operators on ${\mathbb{H}}^{n+1}$
• Existence and asymptotics of nonlinear Helmholtz eigenfunctions
• Nonlinear travelling waves on non-Euclidean spaces
• Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space
• Nonlinear quasimodes near elliptic periodic geodesics
• Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models