Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction. (January 2020)

• Record Type: Journal Article
• Authors: Dinh, Van Duong
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35B35 -- 35B44 -- 35Q55; System NLS quadratic interaction -- Ground states -- Stability -- Blow-up; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111589
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the existence and stability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction in dimensions d ≤ 3 . We also study the characterization of finite time blow-up solutions with minimal mass to the system under mass resonance condition in dimension d = 4 . Finite time blow-up solutions with minimal mass are showed to be (up to symmetries) pseudo-conformal transformations of a ground state standing wave.