The cubic NLS on the line with an inverse square potential

2025/08/03 by Krieger, Joachim, Schlag, Wilhelm, Widmayer, Klaus
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.01919

Abstract

We establish modified scattering for solutions of the cubic NLS on the line with a repulsive inverse square potential and small localized data. The method is based on a comparison between the free and distorted Galilei vector fields and a wave packet transform.

Citations

• On the 1d cubic NLS with a non-generic potential
• Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential
• Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension
• A new proof of long range scattering for critical nonlinear Schrödinger equations
• Decay for the wave and Schroedinger evolutions on manifolds with conical ends, Part II
• Non-generic blow-up solutions for the critical focusing NLS in 1-d

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• Scattering theory for 3d cubic inhomogeneous NLS with inverse square potential
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• Modified scattering for the cubic nonlinear Schrödinger equation with long-range potentials in one space dimension