A note on coupled focusing nonlinear Schrodinger equations

TL;DR

This paper investigates focusing coupled Schrödinger equations, establishing ground state existence, analyzing solution existence via potential-well method, and proving strong instability of standing waves.

Contribution

It provides new results on ground states, solution existence criteria, and instability analysis for coupled focusing Schrödinger equations.

Findings

Existence of ground states confirmed.

Conditions for global and non-global solutions identified.

Strong instability of standing waves proven.

Abstract

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