On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth

Abstract

In this paper, we study the dynamical behavior of solutions of nonlinear Schrödinger equations with quadratic interaction and [Formula: see text]-critical growth. We give sharp conditions under which the existence of global and blow-up solutions are deduced. We also show the existence, stability, and blow-up behavior of normalized solutions of this system.