Failure of scattering for the NLSE with a point interaction in dimension two and three

DOI10.1088/1361-6544/acf1eezbMath1522.35172arXiv2212.14216MaRDI QIDQ6048906

Diego Noja, Domenico Finco, Claudio Cacciapuoti

Publication date: 15 September 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.14216

zbMATH Keywords

scatteringnonlinear Schrödinger equationpoint interactions

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Singularity in context of PDEs (35A21)

Related Items (1)

A general review on the NLS equation with point-concentrated nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations
• \(L^p\)-boundedness of wave operators for the three-dimensional multi-centre point interaction
• Energy methods for abstract nonlinear Schrödinger equations
• Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations
• Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph
• Asymptotic behavior for the long-range nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition
• On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction
• Ground states for the planar NLSE with a point defect as minimizers of the constrained energy
• Well posedness of the nonlinear Schrödinger equation with isolated singularities
• The point-like limit for a NLS equation with concentrated nonlinearity in dimension three
• Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory
• Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
• The asymptotic behavior of nonlinear Schrödinger equations
• Classical Fourier Analysis
• Two-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators
• Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect
• Blow-up and instability of standing waves for the NLS with a point interaction in dimension two

This page was built for publication: Failure of scattering for the NLSE with a point interaction in dimension two and three