Global Dynamics of solutions with group invariance for the nonlinear Schr\"{o}dinger equation

Abstract

We consider the focusing mass-supercritical and energy-subcritical nonlinear Schr\"{o}dinger equation (NLS). We are interested in the global behavior of the solutions to (NLS) with group invariance. By the group invariance, we can determine the global behavior of the solutions above the ground state standing waves.