Scattering for NLS with a potential on the line

DOI10.3233/ASY-161384zbMath1356.35219arXiv1609.01993MaRDI QIDQ2953554

David Lafontaine

Publication date: 4 January 2017

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01993

zbMATH Keywords

scatteringnonlinear Schrödinger equationpotential perturbation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Double scattering channels for 1\(D\) NLS in the energy space and its generalization to higher dimensions ⋮ Scattering theory in homogeneous Sobolev spaces for Schrödinger and wave equations with rough potentials ⋮ Non-radial scattering theory for nonlinear Schrödinger equations with potential ⋮ Scattering of solutions to the nonlinear Schrödinger equations with regular potentials ⋮ Scattering for NLS with a sum of two repulsive potentials ⋮ Global dynamics below the ground state for the focusing semilinear Schrödinger equation with a linear potential ⋮ On the asymptotic behavior of high order moments for a family of Schrödinger equations ⋮ Wave operators on Sobolev spaces ⋮ Scattering for radial defocusing inhomogeneous bi-harmonic Schrödinger equations

Cites Work

• Scattering for a nonlinear Schrödinger equation with a potential
• Scattering for the focusing energy-subcritical nonlinear Schrödinger equation
• Dispersive estimates for Schrödinger operators in dimensions one and three
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• On the decay of solutions to a class of defocusing NLS
• Scattering for the nonradial 3D cubic nonlinear Schrödinger equation
• The lack of compactness in the Sobolev-Strichartz inequalities
• Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2
• A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation
• Scattering for NLS with a delta potential
• Bilinear virial identities and applications
• Tensor products and correlation estimates with applications to nonlinear Schrödinger equations
• Endpoint Strichartz estimates
• INHOMOGENEOUS STRICHARTZ ESTIMATES