Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation

2021/04/20 by Chengbin Xu, Xu, Chengbin · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.09756

openalex publication_date 2021/04/20 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the long-time behavior of global solutions to the Schrödinger-Choquard equation i∂_tu+Δu=-(I_α∗|⋅|^b|u|^p)|⋅|^b|u|^p-2u. Inspired by Murphy, who gave a simple proof of scattering for the non-radial inhomogeneous NLS, we prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.

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• Scattering for the non-radial inhomogeneous Hartree equation with a potential

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