On coupled nonlinear Schrodinger equations with harmonic potential

TL;DR

This paper studies coupled nonlinear Schrödinger equations with harmonic potential, establishing conditions for global solutions, existence of ground states, and stability properties of standing waves.

Contribution

It provides new results on global well-posedness, ground state existence, and instability analysis for coupled nonlinear Schrödinger systems with unbounded potential.

Findings

Global well-posedness in the defocusing case

Existence of ground states and instability of standing waves

Discussion of global and non-global solutions in the focusing case

Abstract

The initial value problem for some coupled nonlinear Schrodinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. For the focusing sign, existence of global and non global solutions is discussed via potential well method. Moreover, existence of ground state and instability of standing waves are proved.