Scattering for the focusing, L²-supercritical fourth-order NLS in one dimension

2023/06/21 by Koichi Komada, Komada, Koichi, Satoshi Masaki +1
Mathematics · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2306.12068

openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the fourth-order Schrödinger equations with focusing, L²-supercritical nonlinearity in one dimension. We prove the global existence and scattering of solutions below the ground state threshold under the evenness assumption. This results extends to the result by Guo and Dinh in higher dimensions under the radial assumption.

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