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arXiv · 2507.14571

Scattering for the nonlinear Schr\"odinger equation with concentrated nonlinearity

Benjamin Harrop-Griffiths·Rowan Killip·Monica Visan
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Abstract

We consider the cubic defocusing nonlinear Schr\"odinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space.

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Benjamin Harrop-Griffiths, Rowan Killip, Monica Visan. 2025-07-19. Scattering for the nonlinear Schr\"odinger equation with concentrated nonlinearity. https://arxiv.org/abs/2507.14571

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