Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation

DOI10.1016/j.jmaa.2023.127016OpenAlexW4315645228MaRDI QIDQ2685250

David E. Grow, Jason Murphy, Christopher C. Hogan

Publication date: 20 February 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.06047

zbMATH Keywords

inverse problemNLS

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Recovery of a spatially-dependent coefficient from the NLS scattering map ⋮ Stability estimates for the recovery of the nonlinearity from scattering data ⋮ On recovering the nonlinearity for generalized higher-order Schrödinger equations

Cites Work

• Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly
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• Time-dependent method for non-linear Schrödinger equations in inverse scattering problems
• \(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
• Inverse scattering for critical semilinear wave equations
• Recovery of a cubic non-linearity in the wave equation in the weakly non-linear regime
• Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case
• Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations
• On a nonlinear scattering operator
• The scattering map determines the nonlinearity
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