Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold

PHYSICA D-NONLINEAR PHENOMENA

卷:425

Article

Ardila, Alex H.¹ 

[1] Univ Fed Minas Gerais, ICEx UFMG, BR-30123970 Belo Horizonte, MG, Brazil

关键词: NLS with point nonlinearity;    Ground state;    Scattering;    Compactness;   

DOI  :  10.1016/j.physd.2021.132978

来源: Elsevier

【 摘 要 】

In this paper, we study the nonlinear Schrodinger equation with focusing point nonlinearity in dimension one. First, we establish a scattering criterion for the equation based on Kenig-Merle's compactness-rigidity argument. Then we prove the energy scattering below and above the mass-energy threshold. We also describe the dynamics of solutions with data at the ground state threshold. Finally, we prove a blow-up criteria for the equation with initial data with arbitrarily large energy. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free