A note on coupled focusing nonlinear Schrödinger equations

Abstract

Some focusing coupled Schrödinger equations are investigated. First, existence of ground state is obtained. Second, global existence and finite-time blow-up of solutions are discussed via potential well method. Finally, strong instability of standing waves is established.

Keywords:

• Nonlinear Schrödinger system
• ground state
• potential well
• global existence
• blow-up
• instability

AMS SUBJECT CLASSIFICATION:

• 35Q55

Notes

No potential conflict of interest was reported by the author.