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