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

TL;DR

This paper investigates the long-term behavior of solutions to the focusing mass-supercritical, energy-subcritical nonlinear Schrödinger equation with group invariance, revealing insights into solutions above ground state standing waves.

Contribution

It establishes the global dynamics of solutions with group invariance for the nonlinear Schrödinger equation in a specific mass and energy regime, extending understanding beyond ground states.

Findings

Characterization of global behavior for solutions with group invariance.

Analysis of solutions above the ground state standing waves.

Insights into the influence of group invariance on solution dynamics.

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.