Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity

2025/07/19 by Harrop-Griffiths, Benjamin, Killip, Rowan, Visan, Monica · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.14571

Abstract

We consider the cubic defocusing nonlinear Schrödinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space L²(ℝ) and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space.

Cited by

• Scattering for the 2d NLS with inhomogeneous nonlinearities
• Scattering for the 1d NLS with inhomogeneous nonlinearities
• Well-posedness of the periodic nonlinear Schrödinger equation with concentrated nonlinearity
• Asymptotic behavior of mass-critical Schrödinger equation in ℝ

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