Modified Scattering for the Hartree Nonlinear Schrödinger Equation

2024/07/25 by Tim Van Hoose, Van Hoose, Tim · 1 citation
Mathematics · Physics and Astronomy · #35P25 (Primary) 35Q55 (Secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2407.18411

openalex publication_date 2024/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove sharp L^∞ decay and modified scattering for the Hartree nonlinear Schrödinger equation in dimensions 2 and 3 using the testing by wavepackets method of Ifrim and Tataru. We show that the scattering behavior happens at a regularity well below that of earlier results of Hayashi-Naumkin and Kato-Pusateri.

Cited by

• Long-Time Dynamics and Modified Scattering for the Coulomb Vlasov--Hartree System

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