Well-posedness and scattering of odd solutions for the defocusing INLS in one dimension

2025/09/02 by Yuan Li, Cui, Zhi-Yuan, Li, Yuan +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.02158

Abstract

We consider the defocusing inhomogeneous nonlinear Schrödinger equation i∂_tu+Δu= |x|^-b|u|^αu, where 0<b></b>

Citations

• Decay of solutions to one-dimensional inhomogeneous nonlinear Schrödinger equations
• Global well-posedness and scattering of the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation with radial data
• An improved one-dimensional Hardy inequality
• Long time dynamics of non-radial solutions to inhomogeneous nonlinear\n Schr "odinger equations
• A Virial-Morawetz approach to scattering for the non-radial inhomogeneous NLS
• Energy scattering for a class of inhomogeneous nonlinear Schr "odinger\n equation in two dimensions
• On well-posedness for the inhomogeneous nonlinear Schrödinger equation in the critical case
• On the GWP of focusing energy-ciritical inhomogeneous NLS
• Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Scattering theory in a weighted L² space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Scattering for the radial 3D cubic focusing inhomogeneous nonlinear\n Schr "odinger equation
• On the decay of solutions to a class of defocusing NLS
• Scattering for the non-radial 3D cubic nonlinear Schroedinger equation
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in \R¹⁺⁴
• Inhomogeneous Strichartz estimates

Cited by

• Scattering for the 2d NLS with inhomogeneous nonlinearities
• Scattering for the 1d NLS with inhomogeneous nonlinearities

Related

• Scattering theory in a weighted L² space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Global well-posedness and scattering of the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation with radial data
• Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension
• On defocusing coupled nonlinear Schrodinger equations