Modified Scattering for the One-Dimensional Cubic NLS with a Repulsive Delta Potential

DOI10.1093/imrn/rny011zbMath1479.35812arXiv1708.00392OpenAlexW2790957084MaRDI QIDQ5015541

Jun-Ichi Segata, Satoshi Masaki, Jason Murphy

Publication date: 9 December 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.00392

zbMATH Keywords

scatteringcubic nonlinear Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (11)

Quadratic Klein-Gordon equations with a potential in one dimension ⋮ The 1-dimensional nonlinear Schrödinger equation with a weighted \(L^1\) potential ⋮ Mini-workshop: Zero-range and point-like singular perturbations: for a spillover to analysis, PDE and differential geometry. Abstracts from the mini-workshop held October 2--8, 2022 ⋮ Asymptotic stability of the sine-Gordon kink under odd perturbations ⋮ On the \(1d\) cubic NLS with a non-generic potential ⋮ Minimal Mass Blow-Up Solutions for the \(\boldsymbol{L}^{\boldsymbol{2}}\)-Critical NLS with the Delta Potential for Even Data in One Dimension ⋮ A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II ⋮ On Stability of Small Solitons of the 1-D NLS with a Trapping Delta Potential ⋮ Stability of small solitary waves for the one-dimensional NLS with an attractive delta potential ⋮ Asymptotic behavior for the long-range nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition ⋮ On selection of standing wave at small energy in the 1D cubic Schrödinger equation with a trapping potential

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