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arXiv · 2610.13753

Scattering for the KP-II equation

Xi Chen
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Abstract

We prove scattering in $L^2(\mathbb{R}^2)$ for real-valued solutions of the Kadomtsev--Petviashvili II (KP-II) equation with localized initial data. No smallness assumption is made, no zero mean condition is imposed, and the admissible data include all Schwartz functions. The proof uses the inverse scattering transform attached to the heat operator. It rests on three ingredients: an a priori bound for the scalar $\bar\partial$ problem which depends on the size of the scattering coefficient but not on its oscillating phase, a nonlinear Plancherel identity proved by analytic continuation from small data, and an estimate showing that the nonlinear part of the reconstruction is negligible on the propagation cones of free waves. To the best of our knowledge, this is the first result establishing scattering for the KP-II equation for every real-valued Schwartz initial datum.

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Xi Chen. 2026-10-13. Scattering for the KP-II equation. https://arxiv.org/abs/2610.13753

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