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Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity

Year: 2026

Type: article

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 L 2 ( R ) L^2(\mathbb {R}) and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17760

Authors: Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Agence Nationale de la Recherche

Awards: G2438624594, Well-Posedness for Integrable Dispersive Partial Differential Equations, The mathematical physics of completely integrable Hamiltonian PDE, G5324346008, The Mathematical Physics of Completely Integrable Hamiltonian Partial Differential Equations, Analytical Challenges Near Dynamical Thresholds for Nonlinear Wave and Fluid Equations, G7138252201, G7160558289, Integrable Partial Differential Equations as Pathfinders in Mathematical Physics, G7616365299, G8726184449, Well-posedness and Long-time Behavior of Dispersive Integrable Systems

OpenAlex ID: W4417429524

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