The nonlinear Schrödinger equation with a potential

DOI10.1016/j.anihpc.2017.12.002zbMath1406.35355arXiv1704.00061OpenAlexW2799474194MaRDI QIDQ1669638

Frédéric Rousset, Pierre Germain, Fabio Pusateri

Publication date: 3 September 2018

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.00061

zbMATH Keywords

global solutionscattering theorymodified scatteringnonlinear cubic Schrödinger equationdistorted Fourier transformgeneric potential

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Resonance in context of PDEs (35B34)

Related Items (19)

Quadratic Klein-Gordon equations with a potential in one dimension ⋮ The 1-dimensional nonlinear Schrödinger equation with a weighted \(L^1\) potential ⋮ Nonlinear waves and dispersive equations. Abstracts from the workshop held June 26 -- July 2, 2022 ⋮ Asymptotic stability of the sine-Gordon kink under odd perturbations ⋮ Stability of traveling waves for the Burgers-Hilbert equation ⋮ On the \(1d\) cubic NLS with a non-generic potential ⋮ On 1d quadratic Klein-Gordon equations with a potential and symmetries ⋮ Asymptotic stability near the soliton for quartic Klein-Gordon equation in 1D ⋮ The matrix nonlinear Schrödinger equation with a potential ⋮ Asymptotic stability of small ground states for NLS under random perturbations ⋮ On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D ⋮ Decay and Asymptotics for the One-Dimensional Klein--Gordon Equation with Variable Coefficient Cubic Nonlinearities ⋮ Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities ⋮ Decay of small odd solutions for long range Schrödinger and Hartree equations in one dimension ⋮ On Stability of Small Solitons of the 1-D NLS with a Trapping Delta Potential ⋮ On selection of standing wave at small energy in the 1D cubic Schrödinger equation with a trapping potential ⋮ Dispersive estimates for nonlinear Schrödinger equations with external potentials ⋮ Wave and scattering operators for the nonlinear matrix Schrödinger equation on the half-line with a potential ⋮ Pointwise dispersive estimates for Schrödinger operators on product cones

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