Threshold solutions for the focusing L² -supercritical NLS Equations

2011/11/24 by Qing Guo, Guo, Qing
Mathematics · Physics and Astronomy · #35A15 #35B30 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1111.5669

openalex publication_date 2011/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the L²-supercritical and H¹-subcritical nonlinear Schrödinger equation in H¹. In \citeG1 and \citeyuan, the mass-energy quantity M(Q)^\frac1-s_cs_cE(Q) has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present paper, we study the dynamics at the critical level M(u)^\frac1-s_cs_cE(u)=M(Q)^\frac1-s_cs_cE(Q) and classify the corresponding solutions using modulation theory, non-trivially generalize the results obtained in \citeholmer3 for the 3D cubic Schrödinger equation.

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