On scattering for NLS: from Euclidean to hyperbolic space

DOI10.3934/dcds.2009.24.1113zbMath1168.35316arXiv0801.2227OpenAlexW1965038885MaRDI QIDQ833264

Rémi Carles, Thomas Duyckaerts, Valeria Banica

Publication date: 12 August 2009

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.2227

zbMATH Keywords

nonlinear Schrödinger equationhyperbolic spacescattering theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum scattering theory (81U99)

Related Items (13)

Profile decompositions for wave equations on hyperbolic space with applications ⋮ Semilinear Schrödinger flows on hyperbolic spaces: scattering in \(H^{1}\) ⋮ MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS ⋮ Global Well-Posedness and Scattering for Mass-Critical, Defocusing, Infinite Dimensional Vector-Valued Resonant Nonlinear Schrödinger System ⋮ Uniqueness of the ground state of the NLS on \(\mathbb{H}^d\) via analytical and topological methods ⋮ Modified scattering and beating effect for coupled Schrödinger systems on product spaces with small initial data ⋮ Scattering for nonlinear Schrödinger equation under partial harmonic confinement ⋮ Nonlinear waves on 3D hyperbolic space ⋮ Global regularity for the energy-critical NLS on \(\mathbb S^3\) ⋮ Minimal Blow-Up Solutions to the Mass-Critical Inhomogeneous NLS Equation ⋮ Qualitative properties of stationary solutions of the NLS on the hyperbolic space without and with external potentials ⋮ On Scattering for the Quintic Defocusing Nonlinear Schrödinger Equation on R × T² ⋮ Dispersive estimates for scalar and matrix Schrödinger operators on \(\mathbb H^{n+1}\)

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