Scattering theory for quadratic nonlinear Schrödinger system in dimension six

In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr & ouml;dinger system in H (center dot) 1 x H (center dot) 1 , where the sign of its potential energy can not be determined directly. If the initial data u0 0 is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of u0 0 is below or above that of the ground state. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.